{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# AdS Poincaré horizon as a degenerate Killing horizon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook demonstrates some capabilities of [SageMath](https://www.sagemath.org/) in computations regarding the Poincaré horizon of the 4-dimensional anti-de Sitter spacetime. It also provides computations and figures for Example 17 of Chap. 3 of the lecture notes [Geometry and physics of black holes](https://luth.obspm.fr/~luthier/gourgoulhon/bh16/). \n", "\n", "The corresponding tools have been developed within the [SageManifolds](https://sagemanifolds.obspm.fr) project." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.5.beta1, Release Date: 2021-09-13'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX rendering and we ask for running tensor computations in parallel on 8 threads:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex\n", "Parallelism().set(nproc=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spacetime manifold\n", "\n", "We declare the anti-de Sitter spacetime as a 4-dimensional Lorentzian manifold:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathscr{M}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathscr{M}$$" ], "text/plain": [ "4-dimensional Lorentzian manifold M" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = Manifold(4, 'M', latex_name=r'\\mathscr{M}', structure='Lorentzian')\n", "print(M)\n", "M" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and endow it with the **conformal coordinates** $(\\tau, \\chi, \\theta,\\phi)$\n", "(cf. the generic [anti-de Sitter notebook](https://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Notebooks/SM_anti_de_Sitter.ipynb)):" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (M, (ta, ch, th, ph))\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{M},({\\tau}, {\\chi}, {\\theta}, {\\phi})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{M},({\\tau}, {\\chi}, {\\theta}, {\\phi})\\right)$$" ], "text/plain": [ "Chart (M, (ta, ch, th, ph))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_conf. = M.chart(r'ta:\\tau ch:(0,pi/2):\\chi th:(0,pi):\\theta ph:(0,2*pi):periodic:\\phi')\n", "print(X_conf)\n", "X_conf" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\frac{1}{2} \\, \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\frac{1}{2} \\, \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}$$" ], "text/plain": [ "ta: (-oo, +oo); ch: (0, 1/2*pi); th: (0, pi); ph: [0, 2*pi] (periodic)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_conf.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spacetime metric" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First of all, we declare the AdS length scale $\\ell$ as a symbolic variable:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "var('l', latex_name=r'\\ell', domain='real')\n", "assume(l>0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we define the metric tensor $g$ by providing its nonzero components:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = -\\frac{{\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} + \\frac{{\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\frac{{\\ell}^{2} \\sin\\left({\\chi}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\ell}^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = -\\frac{{\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} + \\frac{{\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\frac{{\\ell}^{2} \\sin\\left({\\chi}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\ell}^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "g = -l^2/cos(ch)^2 dta⊗dta + l^2/cos(ch)^2 dch⊗dch + l^2*sin(ch)^2/cos(ch)^2 dth⊗dth + l^2*sin(ch)^2*sin(th)^2/cos(ch)^2 dph⊗dph" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = M.metric()\n", "g[0,0] = -l^2/cos(ch)^2\n", "g[1,1] = l^2/cos(ch)^2\n", "g[2,2] = l^2/cos(ch)^2*sin(ch)^2\n", "g[3,3] = l^2/cos(ch)^2*sin(ch)^2*sin(th)^2\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that $g$ is a solution of the vaccum **Einstein equation** with the cosmological constant\n", "$\\Lambda = - 3 /\\ell^2$:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "R = g.ricci_scalar()\n", "Lambda = -3/l^2\n", "\n", "Ric - 1/2*R*g + Lambda*g == 0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poincaré patch" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **Poincaré patch** is the open subset $\\mathscr{M}_{\\rm P}$ of $\\mathscr{M}$ defined by\n", "$$\\cos\\tau - \\sin\\chi \\sin\\theta \\cos\\phi > 0 \\quad\\mbox{and}\\quad -\\pi < \\tau < \\pi.$$\n", "Hence we declare it as" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset MP of the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathscr{M}_{\\rm P}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathscr{M}_{\\rm P}$$" ], "text/plain": [ "Open subset MP of the 4-dimensional Lorentzian manifold M" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "MP = M.open_subset('MP', latex_name=r'\\mathscr{M}_{\\rm P}', \n", " coord_def={X_conf: [cos(ta) - sin(ch)*sin(th)*cos(ph)>0, ta>-pi, ta\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{M}_{\\rm P},(t, x, y, u)\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{M}_{\\rm P},(t, x, y, u)\\right)$$" ], "text/plain": [ "Chart (MP, (t, x, y, u))" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_Poinc. = MP.chart('t x y u:(0,+oo)')\n", "X_Poinc" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad x :\\ \\left( -\\infty, +\\infty \\right) ;\\quad y :\\ \\left( -\\infty, +\\infty \\right) ;\\quad u :\\ \\left( 0 , +\\infty \\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad x :\\ \\left( -\\infty, +\\infty \\right) ;\\quad y :\\ \\left( -\\infty, +\\infty \\right) ;\\quad u :\\ \\left( 0 , +\\infty \\right)$$" ], "text/plain": [ "t: (-oo, +oo); x: (-oo, +oo); y: (-oo, +oo); u: (0, +oo)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_Poinc.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Poincaré coordinates are defined by their link to the conformal coordinates, which we declare via the method transition_map on the restriction of the conformal coordinates to $\\mathscr{M}_{\\rm P}$, X_conf.restrict(MP):" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & -\\frac{{\\ell} \\sin\\left({\\tau}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)} \\\\ x & = & -\\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)} \\\\ y & = & -\\frac{{\\ell} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)} \\\\ u & = & -\\frac{{\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)\\right)} {\\ell}}{\\cos\\left({\\chi}\\right)} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & -\\frac{{\\ell} \\sin\\left({\\tau}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)} \\\\ x & = & -\\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)} \\\\ y & = & -\\frac{{\\ell} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)} \\\\ u & = & -\\frac{{\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)\\right)} {\\ell}}{\\cos\\left({\\chi}\\right)} \\end{array}\\right.$$" ], "text/plain": [ "t = -l*sin(ta)/(cos(ph)*sin(ch)*sin(th) - cos(ta))\n", "x = -l*sin(ch)*sin(ph)*sin(th)/(cos(ph)*sin(ch)*sin(th) - cos(ta))\n", "y = -l*cos(th)*sin(ch)/(cos(ph)*sin(ch)*sin(th) - cos(ta))\n", "u = -(cos(ph)*sin(ch)*sin(th) - cos(ta))*l/cos(ch)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "conf_to_Poinc = X_conf.restrict(MP).transition_map(X_Poinc, \n", " [l*sin(ta)/(cos(ta) - sin(ch)*sin(th)*cos(ph)),\n", " l*sin(ch)*sin(th)*sin(ph)/(cos(ta) - sin(ch)*sin(th)*cos(ph)),\n", " l*sin(ch)*cos(th)/(cos(ta) - sin(ch)*sin(th)*cos(ph)),\n", " l*(cos(ta) - sin(ch)*sin(th)*cos(ph))/cos(ch)])\n", "conf_to_Poinc.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to help SageMath with simplifications, we explicitly set some assumptions:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "assume(sin(ch)>0, sin(th)>0)\n", "assume(cos(ta) - sin(ch)*sin(th)*cos(ph)>0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We provide the inverse of the coordinate change $(\\tau,\\chi,\\theta,\\phi) \\mapsto (t,x,y,u)$ by means of the method set_inverse:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " ta == -arctan2(2*l^2*sin(ta)/(cos(ph)*sin(ch)*sin(th) - cos(ta)), -2*l^2*cos(ta)/(cos(ph)*sin(ch)*sin(th) - cos(ta))) **failed**\n", " ch == ch *passed*\n", " th == th *passed*\n", " ph == -arctan2(2*l^2*sin(ch)*sin(ph)*sin(th)/(cos(ph)*sin(ch)*sin(th) - cos(ta)), -2*l^2*cos(ph)*sin(ch)*sin(th)/(cos(ph)*sin(ch)*sin(th) - cos(ta))) **failed**\n", " t == t *passed*\n", " x == x *passed*\n", " y == y *passed*\n", " u == u *passed*\n", "NB: a failed report can reflect a mere lack of simplification.\n" ] } ], "source": [ "conf_to_Poinc.set_inverse(atan2(2*l*t, x^2+y^2-t^2+l^2*(1+l^2/u^2)),\n", " acos(2*l^3/u/sqrt((x^2+y^2-t^2+l^2*(1+l^2/u^2))^2 + 4*l^2*t^2)),\n", " acos(2*l*y/sqrt((x^2+y^2-t^2+l^2*(1+l^2/u^2))^2\n", " + 4*l^2*(t^2-l^4/u^2))),\n", " atan2(2*l*x, x^2+y^2-t^2-l^2*(1-l^2/u^2))) " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & \\arctan\\left(2 \\, {\\ell} t, {\\ell}^{2} {\\left(\\frac{{\\ell}^{2}}{u^{2}} + 1\\right)} - t^{2} + x^{2} + y^{2}\\right) \\\\ {\\chi} & = & \\arccos\\left(\\frac{2 \\, {\\ell}^{3}}{\\sqrt{4 \\, {\\ell}^{2} t^{2} + {\\left({\\ell}^{2} {\\left(\\frac{{\\ell}^{2}}{u^{2}} + 1\\right)} - t^{2} + x^{2} + y^{2}\\right)}^{2}} u}\\right) \\\\ {\\theta} & = & \\arccos\\left(\\frac{2 \\, {\\ell} y}{\\sqrt{4 \\, {\\left(t^{2} - \\frac{{\\ell}^{4}}{u^{2}}\\right)} {\\ell}^{2} + {\\left({\\ell}^{2} {\\left(\\frac{{\\ell}^{2}}{u^{2}} + 1\\right)} - t^{2} + x^{2} + y^{2}\\right)}^{2}}}\\right) \\\\ {\\phi} & = & \\arctan\\left(2 \\, {\\ell} x, {\\ell}^{2} {\\left(\\frac{{\\ell}^{2}}{u^{2}} - 1\\right)} - t^{2} + x^{2} + y^{2}\\right) \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & \\arctan\\left(2 \\, {\\ell} t, {\\ell}^{2} {\\left(\\frac{{\\ell}^{2}}{u^{2}} + 1\\right)} - t^{2} + x^{2} + y^{2}\\right) \\\\ {\\chi} & = & \\arccos\\left(\\frac{2 \\, {\\ell}^{3}}{\\sqrt{4 \\, {\\ell}^{2} t^{2} + {\\left({\\ell}^{2} {\\left(\\frac{{\\ell}^{2}}{u^{2}} + 1\\right)} - t^{2} + x^{2} + y^{2}\\right)}^{2}} u}\\right) \\\\ {\\theta} & = & \\arccos\\left(\\frac{2 \\, {\\ell} y}{\\sqrt{4 \\, {\\left(t^{2} - \\frac{{\\ell}^{4}}{u^{2}}\\right)} {\\ell}^{2} + {\\left({\\ell}^{2} {\\left(\\frac{{\\ell}^{2}}{u^{2}} + 1\\right)} - t^{2} + x^{2} + y^{2}\\right)}^{2}}}\\right) \\\\ {\\phi} & = & \\arctan\\left(2 \\, {\\ell} x, {\\ell}^{2} {\\left(\\frac{{\\ell}^{2}}{u^{2}} - 1\\right)} - t^{2} + x^{2} + y^{2}\\right) \\end{array}\\right.$$" ], "text/plain": [ "ta = arctan2(2*l*t, l^2*(l^2/u^2 + 1) - t^2 + x^2 + y^2)\n", "ch = arccos(2*l^3/(sqrt(4*l^2*t^2 + (l^2*(l^2/u^2 + 1) - t^2 + x^2 + y^2)^2)*u))\n", "th = arccos(2*l*y/sqrt(4*(t^2 - l^4/u^2)*l^2 + (l^2*(l^2/u^2 + 1) - t^2 + x^2 + y^2)^2))\n", "ph = arctan2(2*l*x, l^2*(l^2/u^2 - 1) - t^2 + x^2 + y^2)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "conf_to_Poinc.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We note that the Jacobian of the coordinate change is quite involved:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "-\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell}}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & -\\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} \\\\\n", "\\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\tau}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} \\\\\n", "\\frac{{\\ell} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\cos\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right)^{2} - {\\ell} \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & -\\frac{{\\ell} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} \\\\\n", "-\\frac{{\\ell} \\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)} & \\frac{{\\ell} \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) - {\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2}} & -\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right)} & \\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)}\n", "\\end{array}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "-\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell}}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & -\\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} \\\\\n", "\\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\tau}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} \\\\\n", "\\frac{{\\ell} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\cos\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & \\frac{{\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right)^{2} - {\\ell} \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} & -\\frac{{\\ell} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2}} \\\\\n", "-\\frac{{\\ell} \\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)} & \\frac{{\\ell} \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) - {\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2}} & -\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right)} & \\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ -(l*cos(ph)*cos(ta)*sin(ch)*sin(th) - l)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2) l*cos(ch)*cos(ph)*sin(ta)*sin(th)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2) l*cos(ph)*cos(th)*sin(ch)*sin(ta)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2) -l*sin(ch)*sin(ph)*sin(ta)*sin(th)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2)]\n", "[ l*sin(ch)*sin(ph)*sin(ta)*sin(th)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2) l*cos(ch)*cos(ta)*sin(ph)*sin(th)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2) l*cos(ta)*cos(th)*sin(ch)*sin(ph)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2) (l*cos(ph)*cos(ta)*sin(ch)*sin(th) - l*sin(ch)^2*sin(th)^2)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2)]\n", "[ l*cos(th)*sin(ch)*sin(ta)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2) l*cos(ch)*cos(ta)*cos(th)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2) (l*cos(ph)*sin(ch)^2 - l*cos(ta)*sin(ch)*sin(th))/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2) -l*cos(th)*sin(ch)^2*sin(ph)*sin(th)/(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) + cos(ta)^2)]\n", "[ -l*sin(ta)/cos(ch) (l*cos(ta)*sin(ch) - l*cos(ph)*sin(th))/cos(ch)^2 -l*cos(ph)*cos(th)*sin(ch)/cos(ch) l*sin(ch)*sin(ph)*sin(th)/cos(ch)]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "conf_to_Poinc.jacobian()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot of the Poincaré coordinate grid in terms of the conformal coordinates $(\\tau,\\chi)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For plotting purposes, we introduce the 2-dimensional plane $\\mathbb{R}^2$, spanned by\n", "Cartesian coordinates $(\\tau, x_\\chi)$:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{R}^2,({\\tau}, {x_\\chi})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{R}^2,({\\tau}, {x_\\chi})\\right)$$" ], "text/plain": [ "Chart (R^2, (ta, x_ch))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R2 = Manifold(2, 'R^2', latex_name=r'\\mathbb{R}^2')\n", "X2. = R2.chart(r'ta:\\tau x_ch:x_\\chi')\n", "X2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and define the following map from AdS spacetime to $\\mathbb{R}^2$:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathscr{M} & \\longrightarrow & \\mathbb{R}^2 \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {x_\\chi}\\right) = \\left({\\tau}, {\\chi} \\cos\\left({\\phi}\\right)\\right) \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathscr{M} & \\longrightarrow & \\mathbb{R}^2 \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {x_\\chi}\\right) = \\left({\\tau}, {\\chi} \\cos\\left({\\phi}\\right)\\right) \\end{array}$$" ], "text/plain": [ "M → R^2\n", " (ta, ch, th, ph) ↦ (ta, x_ch) = (ta, ch*cos(ph))" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi = M.diff_map(R2, {(X_conf, X2): [ta, ch*cos(ph)]})\n", "Phi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us the grid of coordinates $(t,u)$ for $(x,y)=(0,0)$ in terms of the coordinates $(\\tau,\\chi)$. This is achieved by using the method plot on the chart X_Poinc:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "graph1 = X_Poinc.plot(X2, ambient_coords=(x_ch, ta), mapping=Phi.restrict(MP),\n", " fixed_coords={x: 0, y: 0}, \n", " ranges={t: (-15, 15), u: (0.01, 12)}, parameters={l: 1},\n", " color={t: 'red', u: 'grey'}, number_values={t: 33, u: 25}, \n", " plot_points=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We superpose the plot of the Poincaré horizon and a few labels:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 64 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = polygon([(-pi/2, -pi), (pi/2, 0), (-pi/2, pi)], color='cornsilk')\n", "graph += graph1\n", "graph_hor = plot(pi/2 - ch, (ch, -pi/2, pi/2), color='green',\n", " thickness=3) \\\n", " + plot(ch - pi/2, (ch, -pi/2, pi/2), color='green',\n", " thickness=3) \\\n", " + text(r'$\\mathscr{H}$', (-0.9, 2.85), fontsize=18, color='green')\n", "graph += graph_hor\n", "region_labels = text(r'$\\mathscr{M}$', (1, 2.5), fontsize=18, color='black') \\\n", " + text(r'$\\mathscr{M}_{\\rm P}$', (-0.4, 0.5), fontsize=18, \n", " color='black')\n", "graph += region_labels\n", "\n", "show(graph, frame=True, gridlines=True, figsize=8)\n", "graph.save('neh_AdS_Poincare_patch.pdf', frame=True, \n", " gridlines=True, figsize=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Metric tensor in terms of Poincaré coordinates " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The computation of the metric components with respect to Poincaré coordinates is triggered by the method display when it receives the Poincaré chart X_Poinc as an argument:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = -\\frac{u^{2}}{{\\ell}^{2}} \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{u^{2}}{{\\ell}^{2}} \\mathrm{d} x\\otimes \\mathrm{d} x + \\frac{u^{2}}{{\\ell}^{2}} \\mathrm{d} y\\otimes \\mathrm{d} y + \\frac{{\\ell}^{2}}{u^{2}} \\mathrm{d} u\\otimes \\mathrm{d} u\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = -\\frac{u^{2}}{{\\ell}^{2}} \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{u^{2}}{{\\ell}^{2}} \\mathrm{d} x\\otimes \\mathrm{d} x + \\frac{u^{2}}{{\\ell}^{2}} \\mathrm{d} y\\otimes \\mathrm{d} y + \\frac{{\\ell}^{2}}{u^{2}} \\mathrm{d} u\\otimes \\mathrm{d} u$$" ], "text/plain": [ "g = -u^2/l^2 dt⊗dt + u^2/l^2 dx⊗dx + u^2/l^2 dy⊗dy + l^2/u^2 du⊗du" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_Poinc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Killing vector $\\xi$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the above components of $g$ do not depend of $t$, the coordinate vector $\\displaystyle\\frac{\\partial}{\\partial t}$ is clearly a Killing vector of $(\\mathscr{M}_{\\rm P}, g)$. Its expression in terms the conformal coordinates is" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial t } = \\left( -\\frac{\\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - 1}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\tau} } -\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\frac{\\partial}{\\partial {\\chi} } -\\frac{\\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\tau}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\frac{\\partial}{\\partial {\\theta} } + \\frac{\\sin\\left({\\phi}\\right) \\sin\\left({\\tau}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial t } = \\left( -\\frac{\\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - 1}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\tau} } -\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\frac{\\partial}{\\partial {\\chi} } -\\frac{\\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\tau}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\frac{\\partial}{\\partial {\\theta} } + \\frac{\\sin\\left({\\phi}\\right) \\sin\\left({\\tau}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }$$" ], "text/plain": [ "∂/∂t = -(cos(ph)*cos(ta)*sin(ch)*sin(th) - 1)/l ∂/∂ta - cos(ch)*cos(ph)*sin(ta)*sin(th)/l ∂/∂ch - cos(ph)*cos(th)*sin(ta)/(l*sin(ch)) ∂/∂th + sin(ph)*sin(ta)/(l*sin(ch)*sin(th)) ∂/∂ph" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vt = X_Poinc.frame()[0]\n", "vt.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that $\\xi$ is indeed a Killing vector of $(\\mathcal{M}_{\\rm P}, g)$:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.restrict(MP).lie_derivative(vt).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We note that the components of $\\partial/\\partial t$ with respect to conformal coordinates are smooth functions\n", "of $(\\tau,\\chi,\\theta,\\phi)$ that can be extended beyond $\\mathscr{M}_{\\rm P}$. We may therefore extend $\\partial/\\partial t$ to a vector field $\\xi$ defined on the entire AdS spacetime $\\mathscr{M}$:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\xi = \\left( -\\frac{\\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - 1}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\tau} } -\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\frac{\\partial}{\\partial {\\chi} } -\\frac{\\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\tau}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\frac{\\partial}{\\partial {\\theta} } + \\frac{\\sin\\left({\\phi}\\right) \\sin\\left({\\tau}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\xi = \\left( -\\frac{\\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - 1}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\tau} } -\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\frac{\\partial}{\\partial {\\chi} } -\\frac{\\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\tau}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\frac{\\partial}{\\partial {\\theta} } + \\frac{\\sin\\left({\\phi}\\right) \\sin\\left({\\tau}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }$$" ], "text/plain": [ "xi = -(cos(ph)*cos(ta)*sin(ch)*sin(th) - 1)/l ∂/∂ta - cos(ch)*cos(ph)*sin(ta)*sin(th)/l ∂/∂ch - cos(ph)*cos(th)*sin(ta)/(l*sin(ch)) ∂/∂th + sin(ph)*sin(ta)/(l*sin(ch)*sin(th)) ∂/∂ph" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xi = M.vector_field([vt[i].expr() for i in M.irange()], \n", " name='xi', latex_name=r'\\xi')\n", "xi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that the restriction of $\\xi$ to $\\mathscr{M}_{\\rm P}$ coincides with $\\partial/\\partial t$:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\xi = \\frac{\\partial}{\\partial t }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\xi = \\frac{\\partial}{\\partial t }$$" ], "text/plain": [ "xi = ∂/∂t" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xi.restrict(MP).display(X_Poinc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\xi$ is a global Killing vector:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.lie_derivative(xi).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another view of the same property by forming the **Killing equation** $\\nabla_a \\xi_b + \\nabla_b \\xi_a = 0$:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nabla = g.connection()\n", "\n", "nabla(xi.down(g)).symmetrize().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot of $\\xi$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 235 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = polygon([(-pi/2, -pi), (pi/2, 0), (-pi/2, pi)], color='cornsilk')\n", "\n", "graph += xi.plot(X2, ambient_coords=(x_ch, ta), mapping=Phi,\n", " fixed_coords={th: pi/2}, parameters={l: 1},\n", " ranges={ta: (-pi, pi)}, number_values={ta: 11, ch: 7, ph: 3},\n", " color='red', scale=0.3, arrowsize=2)\n", "\n", "graph += graph_hor\n", "show(graph, frame=True, gridlines=True, figsize=8, aspect_ratio=1)\n", "graph.save(\"neh_AdS_Killing_vec.pdf\", frame=True, gridlines=True, \n", " figsize=8, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $u$ as a scalar field on the whole AdS spacetime" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the Poincaré coordinate $u$ in terms of the conformal coordinates $(\\tau,\\chi,\\theta,\\phi)$\n", "is read as the last component (index 3) of the coordinate transformation conf_to_Poinc, which \n", "implements $(\\tau,\\chi,\\theta,\\phi)\\mapsto (t,x,y,u)$:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(-\\frac{{\\ell} \\sin\\left({\\tau}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)}, -\\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)}, -\\frac{{\\ell} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)}, -\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell} \\cos\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(-\\frac{{\\ell} \\sin\\left({\\tau}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)}, -\\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)}, -\\frac{{\\ell} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)}{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right)}, -\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell} \\cos\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)}\\right)$$" ], "text/plain": [ "(-l*sin(ta)/(cos(ph)*sin(ch)*sin(th) - cos(ta)),\n", " -l*sin(ch)*sin(ph)*sin(th)/(cos(ph)*sin(ch)*sin(th) - cos(ta)),\n", " -l*cos(th)*sin(ch)/(cos(ph)*sin(ch)*sin(th) - cos(ta)),\n", " -(l*cos(ph)*sin(ch)*sin(th) - l*cos(ta))/cos(ch))" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "conf_to_Poinc(ta, ch, th, ph)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell} \\cos\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell} \\cos\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)}$$" ], "text/plain": [ "-(l*cos(ph)*sin(ch)*sin(th) - l*cos(ta))/cos(ch)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "conf_to_Poinc(ta, ch, th, ph)[3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This expression being regular in all $\\mathscr{M}$, we may extend $u$ to a scalar field defined on $\\mathscr{M}$ by" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} u:& \\mathscr{M} & \\longrightarrow & \\mathbb{R} \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell} \\cos\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)} \\\\ \\mbox{on}\\ \\mathscr{M}_{\\rm P} : & \\left(t, x, y, u\\right) & \\longmapsto & u \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} u:& \\mathscr{M} & \\longrightarrow & \\mathbb{R} \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - {\\ell} \\cos\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)} \\\\ \\mbox{on}\\ \\mathscr{M}_{\\rm P} : & \\left(t, x, y, u\\right) & \\longmapsto & u \\end{array}$$" ], "text/plain": [ "u: M → ℝ\n", " (ta, ch, th, ph) ↦ -(l*cos(ph)*sin(ch)*sin(th) - l*cos(ta))/cos(ch)\n", "on MP: (t, x, y, u) ↦ u" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U = M.scalar_field(conf_to_Poinc(ta, ch, th, ph)[3], name='u')\n", "U.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Poincaré horizon as the submanifold $u=0$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **Poincaré horizon** \n", "is the hypersurface $\\mathscr{H}$ bounding the Poincaré patch $\\mathscr{M}_{\\rm P}$ in \n", "$\\mathscr{M}$. It follows that $\\mathscr{H}$ is the level set $u=0$ within the region $-\\pi<\\tau<\\pi$.\n", "$\\mathscr{H}$ has actually two connected components: one for $-\\pi < \\tau < 0$ and the other one\n", "for $0 < \\tau <\\pi$. In what follows, we focus on the connected component that has $0 < \\tau <\\pi$; we define\n", "it as a submanifold of $\\mathscr{M}$, by means of the keyword ambient in the function Manifold:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3-dimensional differentiable submanifold H immersed in the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "H = Manifold(3, 'H', ambient=M, latex_name=r'\\mathscr{H}')\n", "print(H)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider that $\\mathscr{H}$ is spanned by the coordinates $(\\chi,\\theta,\\phi)$, so that we declare the following \n", "chart:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{H},({\\chi}, {\\theta}, {\\phi})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{H},({\\chi}, {\\theta}, {\\phi})\\right)$$" ], "text/plain": [ "Chart (H, (ch, th, ph))" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XH. = H.chart(r'ch:(0,pi/2):\\chi th:(0,pi):\\theta ph:(0,2*pi):periodic:\\phi')\n", "XH" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **embedding $F$ of** $\\mathscr{H}$ **into** $\\mathscr{M}$ is easily defined in the pair of charts\n", "(XH, X_conf) by noticing that, for $0 < \\tau <\\pi$, $u=0 \\iff \\tau = \\arccos(\\sin\\chi\\sin\\theta\\cos\\phi)$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} F:& \\mathscr{H} & \\longrightarrow & \\mathscr{M} \\\\ & \\left({\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arccos\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)\\right), {\\chi}, {\\theta}, {\\phi}\\right) \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} F:& \\mathscr{H} & \\longrightarrow & \\mathscr{M} \\\\ & \\left({\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arccos\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)\\right), {\\chi}, {\\theta}, {\\phi}\\right) \\end{array}$$" ], "text/plain": [ "F: H → M\n", " (ch, th, ph) ↦ (ta, ch, th, ph) = (arccos(cos(ph)*sin(ch)*sin(th)), ch, th, ph)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F = H.diff_map(M, {(XH, X_conf): (acos(sin(ch)*sin(th)*cos(ph)), ch, th, ph)},\n", " name='F')\n", "F.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We declare that $F$ is the embedding of $\\mathscr{H}$ into $\\mathscr{M}$, thereby ending the definition of $\\mathscr{H}$:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3-dimensional differentiable submanifold H embedded in the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "H.set_embedding(F)\n", "print(H)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may check that the scalar field $u$ is zero on $\\mathscr{H}$ by considering the pullback of $u$ by $F$:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field F^*(u) on the 3-dimensional differentiable submanifold H embedded in the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "FU = F.pullback(U)\n", "print(FU)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} {F}^*u:& \\mathscr{H} & \\longrightarrow & \\mathbb{R} \\\\ & \\left({\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 0 \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} {F}^*u:& \\mathscr{H} & \\longrightarrow & \\mathbb{R} \\\\ & \\left({\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 0 \\end{array}$$" ], "text/plain": [ "F^*(u): H → ℝ\n", " (ch, th, ph) ↦ 0" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "FU.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Null character of the hypersurface $\\mathscr{H}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The metric induced by $g$ on $\\mathscr{H}$ is obtained as the pullback of $g$ by the embedding $F$:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field of symmetric bilinear forms F^*(g) on the 3-dimensional differentiable submanifold H embedded in the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "Fg = F.pullback(g)\n", "print(Fg)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{F}^*g = \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - {\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\phi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\chi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{4} \\sin\\left({\\theta}\\right)^{2} + {\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} - {\\ell}^{2} \\sin\\left({\\chi}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\phi} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\chi} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{4} \\sin\\left({\\theta}\\right)^{4} - {\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{F}^*g = \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - {\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\phi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\chi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{4} \\sin\\left({\\theta}\\right)^{2} + {\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} - {\\ell}^{2} \\sin\\left({\\chi}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\phi} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\chi} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{4} \\sin\\left({\\theta}\\right)^{4} - {\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "F^*(g) = (l^2*cos(ph)^2*sin(th)^2 - l^2)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dch⊗dch + l^2*cos(ph)^2*cos(th)*sin(ch)*sin(th)/(cos(ch)*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)) dch⊗dth - l^2*cos(ph)*sin(ch)*sin(ph)*sin(th)^2/(cos(ch)*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)) dch⊗dph + l^2*cos(ph)^2*cos(th)*sin(ch)*sin(th)/(cos(ch)*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)) dth⊗dch + (l^2*cos(ph)^2*sin(ch)^4*sin(th)^2 + l^2*cos(ph)^2*cos(th)^2*sin(ch)^2 - l^2*sin(ch)^2)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dth⊗dth - l^2*cos(ph)*cos(th)*sin(ch)^2*sin(ph)*sin(th)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dth⊗dph - l^2*cos(ph)*sin(ch)*sin(ph)*sin(th)^2/(cos(ch)*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)) dph⊗dch - l^2*cos(ph)*cos(th)*sin(ch)^2*sin(ph)*sin(th)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dph⊗dth + (l^2*cos(ph)^2*sin(ch)^4*sin(th)^4 - l^2*cos(ph)^2*sin(ch)^2*sin(th)^2)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dph⊗dph" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Fg.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We declare a metric $h$ on $\\mathscr{H}$ and initialize it with the pullback $F^* g$:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - {\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\phi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\chi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{4} \\sin\\left({\\theta}\\right)^{2} + {\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} - {\\ell}^{2} \\sin\\left({\\chi}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\phi} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\chi} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{4} \\sin\\left({\\theta}\\right)^{4} - {\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - {\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\phi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\chi} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{4} \\sin\\left({\\theta}\\right)^{2} + {\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} - {\\ell}^{2} \\sin\\left({\\chi}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\phi} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\chi} + \\left( -\\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{{\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{4} \\sin\\left({\\theta}\\right)^{4} - {\\ell}^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "h = (l^2*cos(ph)^2*sin(th)^2 - l^2)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dch⊗dch + l^2*cos(ph)^2*cos(th)*sin(ch)*sin(th)/(cos(ch)*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)) dch⊗dth - l^2*cos(ph)*sin(ch)*sin(ph)*sin(th)^2/(cos(ch)*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)) dch⊗dph + l^2*cos(ph)^2*cos(th)*sin(ch)*sin(th)/(cos(ch)*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)) dth⊗dch + (l^2*cos(ph)^2*sin(ch)^4*sin(th)^2 + l^2*cos(ph)^2*cos(th)^2*sin(ch)^2 - l^2*sin(ch)^2)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dth⊗dth - l^2*cos(ph)*cos(th)*sin(ch)^2*sin(ph)*sin(th)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dth⊗dph - l^2*cos(ph)*sin(ch)*sin(ph)*sin(th)^2/(cos(ch)*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)) dph⊗dch - l^2*cos(ph)*cos(th)*sin(ch)^2*sin(ph)*sin(th)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dph⊗dth + (l^2*cos(ph)^2*sin(ch)^4*sin(th)^4 - l^2*cos(ph)^2*sin(ch)^2*sin(th)^2)/(cos(ch)^2*cos(ph)^2*sin(ch)^2*sin(th)^2 - cos(ch)^2) dph⊗dph" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = H.metric('h')\n", "h.set(Fg)\n", "h.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a degenerate metric:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathscr{H} & \\longrightarrow & \\mathbb{R} \\\\ & \\left({\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 0 \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathscr{H} & \\longrightarrow & \\mathbb{R} \\\\ & \\left({\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 0 \\end{array}$$" ], "text/plain": [ "H → ℝ\n", "(ch, th, ph) ↦ 0" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.determinant().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence the Poincaré horizon $\\mathscr{H}$ is a **null hypersurface**. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The normal to the Poincaré horizon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since $\\mathscr{H}$ is the isosurface $u=0$, its normal $k$ is defined as the gradient of $u$:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}u = -\\frac{{\\ell} \\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)} \\mathrm{d} {\\tau} + \\left( \\frac{{\\ell} \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) - {\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\chi} -\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right)} \\mathrm{d} {\\theta} + \\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)} \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}u = -\\frac{{\\ell} \\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right)} \\mathrm{d} {\\tau} + \\left( \\frac{{\\ell} \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) - {\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\chi} -\\frac{{\\ell} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right)} \\mathrm{d} {\\theta} + \\frac{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\chi}\\right)} \\mathrm{d} {\\phi}$$" ], "text/plain": [ "du = -l*sin(ta)/cos(ch) dta + (l*cos(ta)*sin(ch) - l*cos(ph)*sin(th))/cos(ch)^2 dch - l*cos(ph)*cos(th)*sin(ch)/cos(ch) dth + l*sin(ch)*sin(ph)*sin(th)/cos(ch) dph" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dU = diff(U)\n", "dU.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "dU is a 1-form; we turn it into a vector field by raising its index with the metric $g$, via the method up:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\frac{\\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)}{{\\ell}} \\frac{\\partial}{\\partial {\\tau} } + \\left( \\frac{\\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) - \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\chi} } -\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\frac{\\partial}{\\partial {\\theta} } + \\frac{\\cos\\left({\\chi}\\right) \\sin\\left({\\phi}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\frac{\\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)}{{\\ell}} \\frac{\\partial}{\\partial {\\tau} } + \\left( \\frac{\\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) - \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\chi} } -\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\frac{\\partial}{\\partial {\\theta} } + \\frac{\\cos\\left({\\chi}\\right) \\sin\\left({\\phi}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }$$" ], "text/plain": [ "k = cos(ch)*sin(ta)/l ∂/∂ta + (cos(ta)*sin(ch) - cos(ph)*sin(th))/l ∂/∂ch - cos(ch)*cos(ph)*cos(th)/(l*sin(ch)) ∂/∂th + cos(ch)*sin(ph)/(l*sin(ch)*sin(th)) ∂/∂ph" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = dU.up(g)\n", "k.set_name('k')\n", "k.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot of $k$:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 236 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = k.plot(X2, ambient_coords=(x_ch, ta), mapping=Phi,\n", " fixed_coords={th: pi/2}, parameters={l: 1},\n", " ranges={ta: (-pi, pi)}, number_values={ta: 11, ch: 7, ph: 3},\n", " color='orange', scale=0.3, arrowsize=2)\n", "graph += graph_hor\n", "graph += line([(-pi/2, -pi), (-pi/2, pi)], color='black')\n", "graph += line([(pi/2, -pi), (pi/2, pi)], color='black')\n", "show(graph, frame=True, gridlines=True, figsize=8, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We note that, graphically, $k$ appears tangent to $\\mathscr{H}$, in agreement with $\\mathscr{H}$ being a null hypersurface (the only kind of hypersurface for which the normal is also tangent to the hypersurface)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The spacetime metric $g$ restricted to $\\mathscr{H}$ is evaluated by means of the method along:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lorentzian metric g_H along the 3-dimensional differentiable submanifold H embedded in the 4-dimensional Lorentzian manifold M with values on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "g_H = H.lorentzian_metric('g_H', latex_name=r'\\left.g\\right|_{\\mathscr{H}}', \n", " dest_map=F)\n", "g_H.set(g.along(F))\n", "print(g_H)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left.g\\right|_{\\mathscr{H}} = -\\frac{{\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} + \\frac{{\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\frac{{\\ell}^{2} \\sin\\left({\\chi}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\ell}^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left.g\\right|_{\\mathscr{H}} = -\\frac{{\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} + \\frac{{\\ell}^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\frac{{\\ell}^{2} \\sin\\left({\\chi}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\ell}^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "g_H = -l^2/cos(ch)^2 dta⊗dta + l^2/cos(ch)^2 dch⊗dch + l^2*sin(ch)^2/cos(ch)^2 dth⊗dth + l^2*sin(ch)^2*sin(th)^2/cos(ch)^2 dph⊗dph" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_H.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The vector field $k$ restricted to $\\mathscr{H}$:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field k_H along the 3-dimensional differentiable submanifold H embedded in the 4-dimensional Lorentzian manifold M with values on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "k_H = k.along(F)\n", "k_H.set_name('k_H', latex_name=r'\\left.k\\right|_{\\mathscr{H}}')\n", "print(k_H)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left.k\\right|_{\\mathscr{H}} = \\left( \\frac{\\sqrt{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\cos\\left({\\chi}\\right)}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\tau} } -\\frac{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\frac{\\partial}{\\partial {\\chi} } -\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\frac{\\partial}{\\partial {\\theta} } + \\frac{\\cos\\left({\\chi}\\right) \\sin\\left({\\phi}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left.k\\right|_{\\mathscr{H}} = \\left( \\frac{\\sqrt{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\cos\\left({\\chi}\\right)}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\tau} } -\\frac{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\frac{\\partial}{\\partial {\\chi} } -\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\frac{\\partial}{\\partial {\\theta} } + \\frac{\\cos\\left({\\chi}\\right) \\sin\\left({\\phi}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }$$" ], "text/plain": [ "k_H = sqrt(cos(ph)*sin(ch)*sin(th) + 1)*sqrt(-cos(ph)*sin(ch)*sin(th) + 1)*cos(ch)/l ∂/∂ta - cos(ch)^2*cos(ph)*sin(th)/l ∂/∂ch - cos(ch)*cos(ph)*cos(th)/(l*sin(ch)) ∂/∂th + cos(ch)*sin(ph)/(l*sin(ch)*sin(th)) ∂/∂ph" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k_H.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check that $\\left.k\\right|_{\\mathscr{H}}$ is a null vector field:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_H(k_H, k_H).expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since $\\left.k\\right|_{\\mathscr{H}}$ is normal to $\\mathscr{H}$, we recover the fact that $\\mathscr{H}$ is a null hypersurface. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Killing horizon character " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Killing vector field $\\xi$ restricted to $\\mathscr{H}$:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field xi_H along the 3-dimensional differentiable submanifold H embedded in the 4-dimensional Lorentzian manifold M with values on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "xi_H = xi.along(F)\n", "xi_H.set_name('xi_H', latex_name=r'\\left.\\xi\\right|_{\\mathscr{H}}')\n", "print(xi_H)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left.\\xi\\right|_{\\mathscr{H}} = \\left( -\\frac{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 1}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -\\frac{\\sqrt{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\chi} } + \\left( -\\frac{\\sqrt{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\right) \\frac{\\partial}{\\partial {\\theta} } + \\left( \\frac{\\sqrt{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sin\\left({\\phi}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\right) \\frac{\\partial}{\\partial {\\phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left.\\xi\\right|_{\\mathscr{H}} = \\left( -\\frac{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 1}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -\\frac{\\sqrt{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\cos\\left({\\chi}\\right) \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{{\\ell}} \\right) \\frac{\\partial}{\\partial {\\chi} } + \\left( -\\frac{\\sqrt{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right)}{{\\ell} \\sin\\left({\\chi}\\right)} \\right) \\frac{\\partial}{\\partial {\\theta} } + \\left( \\frac{\\sqrt{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) + 1} \\sin\\left({\\phi}\\right)}{{\\ell} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\right) \\frac{\\partial}{\\partial {\\phi} }$$" ], "text/plain": [ "xi_H = -(cos(ph)^2*sin(ch)^2*sin(th)^2 - 1)/l ∂/∂ta - sqrt(cos(ph)*sin(ch)*sin(th) + 1)*sqrt(-cos(ph)*sin(ch)*sin(th) + 1)*cos(ch)*cos(ph)*sin(th)/l ∂/∂ch - sqrt(cos(ph)*sin(ch)*sin(th) + 1)*sqrt(-cos(ph)*sin(ch)*sin(th) + 1)*cos(ph)*cos(th)/(l*sin(ch)) ∂/∂th + sqrt(cos(ph)*sin(ch)*sin(th) + 1)*sqrt(-cos(ph)*sin(ch)*sin(th) + 1)*sin(ph)/(l*sin(ch)*sin(th)) ∂/∂ph" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xi_H.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Value of $\\tau$ on $\\mathscr{H}$:" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\arccos\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\arccos\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)\\right)$$" ], "text/plain": [ "arccos(cos(ph)*sin(ch)*sin(th))" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ta_H = F.expr()[0]\n", "ta_H" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check that\n", "$\\xi \\stackrel{\\mathscr{H}}{=} \\frac{\\sin\\tau}{\\cos\\chi} \\, k$:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xi_H == sin(ta_H)/cos(ch)*k_H" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence, on $\\mathscr{H}$, the Killing vector $\\xi$ is normal to $\\mathscr{H}$. \n", "$\\mathscr{H}$ being a null hypersurface, this implies that $\\mathscr{H}$ **is a Killing horizon**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a consequence, $\\xi$ must be a null vector on $\\mathscr{H}$. We can check this property by computing the scalar square of $\\xi$ in all $\\mathscr{M}$:" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} g\\left(\\xi,\\xi\\right):& \\mathscr{M} & \\longrightarrow & \\mathbb{R} \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\sin\\left({\\tau}\\right)^{2} + 1}{\\cos\\left({\\chi}\\right)^{2}} \\\\ \\mbox{on}\\ \\mathscr{M}_{\\rm P} : & \\left(t, x, y, u\\right) & \\longmapsto & -\\frac{u^{2}}{{\\ell}^{2}} \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} g\\left(\\xi,\\xi\\right):& \\mathscr{M} & \\longrightarrow & \\mathbb{R} \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\sin\\left({\\tau}\\right)^{2} + 1}{\\cos\\left({\\chi}\\right)^{2}} \\\\ \\mbox{on}\\ \\mathscr{M}_{\\rm P} : & \\left(t, x, y, u\\right) & \\longmapsto & -\\frac{u^{2}}{{\\ell}^{2}} \\end{array}$$" ], "text/plain": [ "g(xi,xi): M → ℝ\n", " (ta, ch, th, ph) ↦ -(cos(ph)^2*sin(ch)^2*sin(th)^2 - 2*cos(ph)*cos(ta)*sin(ch)*sin(th) - sin(ta)^2 + 1)/cos(ch)^2\n", "on MP: (t, x, y, u) ↦ -u^2/l^2" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xi2 = g(xi, xi)\n", "xi2.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and notice that it is equal to $-u^2/\\ell^2$:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xi2 == - U^2/l^2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "so that $\\xi$ is null on $\\mathscr{H}$ as a direct consequence of the vanishing of $u$ on $\\mathscr{H}$. Incidentally, the above formula implies that the Killing vector $\\xi$ is timelike everywhere on the AdS spacetime, except on the Poincaré horizon, where it is null. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Degenerate character of the Killing horizon $\\mathscr{H}$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **non-affinity coefficient** $\\kappa$ of $\\xi$ on $\\mathscr{H}$ is defined by $\\nabla_\\xi \\xi \\stackrel{\\mathscr{H}}{=} \\kappa \\xi$. To compute $\\kappa$, we first compute the \"acceleration\" vector\n", "$\\nabla_\\xi \\xi$:" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( -\\frac{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right) \\sin\\left({\\tau}\\right)}{{\\ell}^{2}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -\\frac{\\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right)^{2} \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)^{2} - \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\tau}\\right)^{2} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)^{2} + \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right)^{2} \\sin\\left({\\tau}\\right)^{2} - {\\left(\\cos\\left({\\chi}\\right)^{2} - 2\\right)} \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\theta}\\right) - \\sin\\left({\\chi}\\right)}{{\\ell}^{2} \\cos\\left({\\chi}\\right)} \\right) \\frac{\\partial}{\\partial {\\chi} } + \\left( \\frac{\\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\cos\\left({\\theta}\\right)}{{\\ell}^{2} \\sin\\left({\\chi}\\right)} \\right) \\frac{\\partial}{\\partial {\\theta} } + \\left( -\\frac{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right) \\sin\\left({\\phi}\\right)}{{\\ell}^{2} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\right) \\frac{\\partial}{\\partial {\\phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( -\\frac{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right) \\sin\\left({\\tau}\\right)}{{\\ell}^{2}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -\\frac{\\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right)^{2} \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)^{2} - \\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\tau}\\right)^{2} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)^{2} + \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right)^{2} \\sin\\left({\\tau}\\right)^{2} - {\\left(\\cos\\left({\\chi}\\right)^{2} - 2\\right)} \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\theta}\\right) - \\sin\\left({\\chi}\\right)}{{\\ell}^{2} \\cos\\left({\\chi}\\right)} \\right) \\frac{\\partial}{\\partial {\\chi} } + \\left( \\frac{\\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\cos\\left({\\theta}\\right)}{{\\ell}^{2} \\sin\\left({\\chi}\\right)} \\right) \\frac{\\partial}{\\partial {\\theta} } + \\left( -\\frac{\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right) \\sin\\left({\\phi}\\right)}{{\\ell}^{2} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)} \\right) \\frac{\\partial}{\\partial {\\phi} }$$" ], "text/plain": [ "-(cos(ph)*sin(ch)*sin(ta)*sin(th) - cos(ta)*sin(ta))/l^2 ∂/∂ta - (cos(ph)^2*cos(th)^2*sin(ch)*sin(ta)^2 - cos(ph)^2*cos(ta)^2*sin(ch)*sin(th)^2 + sin(ch)*sin(ph)^2*sin(ta)^2 - (cos(ch)^2 - 2)*cos(ph)*cos(ta)*sin(th) - sin(ch))/(l^2*cos(ch)) ∂/∂ch + (cos(ph)^2*cos(th)*sin(ch)*sin(th) - cos(ph)*cos(ta)*cos(th))/(l^2*sin(ch)) ∂/∂th - (cos(ph)*sin(ch)*sin(ph)*sin(th) - cos(ta)*sin(ph))/(l^2*sin(ch)*sin(th)) ∂/∂ph" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc = nabla(xi).contract(xi)\n", "acc.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and subsquently evaluate it on $\\mathscr{H}$:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc.along(F).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence we get $\\kappa = 0$, so that the Poincaré horizon $\\mathscr{H}$ is a **degenerate Killing horizon**. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that $\\kappa = 0$ can also be obtained via the formula\n", "$$\\mathrm{d}(\\xi\\cdot\\xi) \\stackrel{\\mathscr{H}}{=} -2 \\kappa \\underline{\\xi} .$$\n", "which holds for any Killing horizon. The left hand side is computed as" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}g\\left(\\xi,\\xi\\right) = -\\frac{2 \\, {\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right) \\sin\\left({\\tau}\\right)\\right)}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\tau} -\\frac{2 \\, {\\left(\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)^{2} + {\\left(\\cos\\left({\\chi}\\right)^{2} - 2\\right)} \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2} \\sin\\left({\\chi}\\right)\\right)}}{\\cos\\left({\\chi}\\right)^{3}} \\mathrm{d} {\\chi} -\\frac{2 \\, {\\left(\\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right) - \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)\\right)}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\theta} + \\frac{2 \\, {\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)\\right)}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}g\\left(\\xi,\\xi\\right) = -\\frac{2 \\, {\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\sin\\left({\\theta}\\right) - \\cos\\left({\\tau}\\right) \\sin\\left({\\tau}\\right)\\right)}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\tau} -\\frac{2 \\, {\\left(\\cos\\left({\\phi}\\right)^{2} \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)^{2} + {\\left(\\cos\\left({\\chi}\\right)^{2} - 2\\right)} \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\sin\\left({\\theta}\\right) + \\cos\\left({\\tau}\\right)^{2} \\sin\\left({\\chi}\\right)\\right)}}{\\cos\\left({\\chi}\\right)^{3}} \\mathrm{d} {\\chi} -\\frac{2 \\, {\\left(\\cos\\left({\\phi}\\right)^{2} \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right) - \\cos\\left({\\phi}\\right) \\cos\\left({\\tau}\\right) \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)\\right)}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\theta} + \\frac{2 \\, {\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)^{2} - \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)\\right)}}{\\cos\\left({\\chi}\\right)^{2}} \\mathrm{d} {\\phi}$$" ], "text/plain": [ "dg(xi,xi) = -2*(cos(ph)*sin(ch)*sin(ta)*sin(th) - cos(ta)*sin(ta))/cos(ch)^2 dta - 2*(cos(ph)^2*sin(ch)*sin(th)^2 + (cos(ch)^2 - 2)*cos(ph)*cos(ta)*sin(th) + cos(ta)^2*sin(ch))/cos(ch)^3 dch - 2*(cos(ph)^2*cos(th)*sin(ch)^2*sin(th) - cos(ph)*cos(ta)*cos(th)*sin(ch))/cos(ch)^2 dth + 2*(cos(ph)*sin(ch)^2*sin(ph)*sin(th)^2 - cos(ta)*sin(ch)*sin(ph)*sin(th))/cos(ch)^2 dph" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dxi2 = diff(xi2)\n", "dxi2.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The restriction of this 1-form to $\\mathscr{H}$ is computed by means of the method along:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form dg(xi,xi) along the 3-dimensional differentiable submanifold H embedded in the 4-dimensional Lorentzian manifold M with values on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "dxi2_H = dxi2.along(F)\n", "print(dxi2_H)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}g\\left(\\xi,\\xi\\right) = 0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}g\\left(\\xi,\\xi\\right) = 0$$" ], "text/plain": [ "dg(xi,xi) = 0" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dxi2_H.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence $\\mathrm{d}(\\xi\\cdot\\xi) \\stackrel{\\mathscr{H}}{=} 0$ and we recover $\\kappa=0$." ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5.beta1", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }