{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Anti-de Sitter spacetime\n", "\n", "This notebook demonstrates a few capabilities of SageMath in computations regarding the 4-dimensional anti-de Sitter spacetime. The corresponding tools have been developed within the [SageManifolds](https://sagemanifolds.obspm.fr) project." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 8.2 is required to run this notebook:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.2.beta6, Release Date: 2020-07-25'" ] }, "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:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We initialize a time counter for benchmarking:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import time\n", "comput_time0 = time.perf_counter()" ] }, { "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": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathcal{M}\n", "\\end{math}" ], "text/plain": [ "4-dimensional Lorentzian manifold M" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = Manifold(4, 'M', r'\\mathcal{M}', structure='Lorentzian')\n", "print(M); M" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We consider hyperbolic coordinates $(\\tau,\\rho,\\theta,\\phi)$ on $\\mathcal{M}$. Allowing for the standard coordinate singularities at $\\rho=0$, $\\theta=0$ or $\\theta=\\pi$, these coordinates cover the entire spacetime manifold (which is topologically $\\mathbb{R}^4$). If we restrict ourselves to regular coordinates (i.e. to considering only mathematically well defined charts), the hyperbolic coordinates cover only an open part of $\\mathcal{M}$, which we call $\\mathcal{M}_0$, on which $\\rho$ spans the open interval $(0,+\\infty)$, $\\theta$ the open interval $(0,\\pi)$ and $\\phi$ the open interval $(0,2\\pi)$. Therefore, we declare:

" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (M_0, (ta, rh, th, ph))\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathcal{M}_0,({\\tau}, {\\rho}, {\\theta}, {\\phi})\\right)\n", "\\end{math}" ], "text/plain": [ "Chart (M_0, (ta, rh, th, ph))" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M0 = M.open_subset('M_0', r'\\mathcal{M}_0' )\n", "X_hyp. = M0.chart(r'ta:\\tau rh:(0,+oo):\\rho th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "print(X_hyp); X_hyp" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\rho} :\\ \\left( 0 , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)\n", "\\end{math}" ], "text/plain": [ "ta: (-oo, +oo); rh: (0, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_hyp.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\mathbb{R}^{2,3}$ as an ambient space\n", "The AdS metric can be defined as that induced by the immersion of $\\mathcal{M}$ in $\\mathbb{R}^{2,3}$, the latter being nothing but $\\mathbb{R}^5$ equipped with a flat pseudo-Riemannian metric of signature $(-,-,+,+,+)$. Let us construct $\\mathbb{R}^{2,3}$ as a 5-dimensional manifold covered by canonical coordinates:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (R23, (U, V, X, Y, Z))\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{R}^{2,3},(U, V, X, Y, Z)\\right)\n", "\\end{math}" ], "text/plain": [ "Chart (R23, (U, V, X, Y, Z))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R23 = Manifold(5, 'R23', r'\\mathbb{R}^{2,3}', structure='pseudo-Riemannian', signature=1, \n", " metric_name='h')\n", "X23. = R23.chart()\n", "print(X23); X23" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the pseudo-Riemannian metric of $\\mathbb{R}^{2,3}$:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = -\\mathrm{d} U\\otimes \\mathrm{d} U-\\mathrm{d} V\\otimes \\mathrm{d} V+\\mathrm{d} X\\otimes \\mathrm{d} X+\\mathrm{d} Y\\otimes \\mathrm{d} Y+\\mathrm{d} Z\\otimes \\mathrm{d} Z\n", "\\end{math}" ], "text/plain": [ "h = -dU*dU - dV*dV + dX*dX + dY*dY + dZ*dZ" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = R23.metric()\n", "h[0,0], h[1,1], h[2,2], h[3,3], h[4,4] = -1, -1, 1, 1, 1\n", "h.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The AdS immersion into $\\mathbb{R}^{2,3}$ is defined as a differential map $\\Phi$ from $\\mathcal{M}$ to $\\mathbb{R}^{2,3}$, by providing its expression in terms of $\\mathcal{M}$'s default chart (which is X_hyp = $(\\mathcal{M}_0,(\\tau,\\rho,\\theta,\\phi))$ ) and $\\mathbb{R}^{2,3}$'s default chart (which is X23 = $(\\mathbb{R}^{2,3},(U,V,X,Y,Z))$ ):" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Differentiable map Phi from the 4-dimensional Lorentzian manifold M to the 5-dimensional pseudo-Riemannian manifold R23\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi:& \\mathcal{M} & \\longrightarrow & \\mathbb{R}^{2,3} \\\\ \\mbox{on}\\ \\mathcal{M}_0 : & \\left({\\tau}, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left(U, V, X, Y, Z\\right) = \\left({\\ell} \\cos\\left(\\frac{{\\tau}}{{\\ell}}\\right) \\cosh\\left({\\rho}\\right), {\\ell} \\cosh\\left({\\rho}\\right) \\sin\\left(\\frac{{\\tau}}{{\\ell}}\\right), {\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) \\sinh\\left({\\rho}\\right), {\\ell} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) \\sinh\\left({\\rho}\\right), {\\ell} \\cos\\left({\\theta}\\right) \\sinh\\left({\\rho}\\right)\\right) \\end{array}\n", "\\end{math}" ], "text/plain": [ "Phi: M --> R23\n", "on M_0: (ta, rh, th, ph) |--> (U, V, X, Y, Z) = (l*cos(ta/l)*cosh(rh), l*cosh(rh)*sin(ta/l), l*cos(ph)*sin(th)*sinh(rh), l*sin(ph)*sin(th)*sinh(rh), l*cos(th)*sinh(rh))" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('l', latex_name=r'\\ell', domain='real')\n", "assume(l>0)\n", "Phi = M.diff_map(R23, [l*cosh(rh)*cos(ta/l),\n", " l*cosh(rh)*sin(ta/l),\n", " l*sinh(rh)*sin(th)*cos(ph),\n", " l*sinh(rh)*sin(th)*sin(ph),\n", " l*sinh(rh)*cos(th)],\n", " name='Phi', latex_name=r'\\Phi')\n", "print(Phi); Phi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The constant $\\ell$ is the AdS length parameter. Considering AdS metric as a solution of vacuum Einstein equation with negative cosmological constant $\\Lambda$, one has $\\ell = \\sqrt{-3/\\Lambda}$.\n", "\n", "Let us evaluate the image of a point via the map $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point p on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "p = M((ta, rh, th, ph), name='p'); print(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coordinates of $p$ in the chart `X_hyp`:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left({\\tau}, {\\rho}, {\\theta}, {\\phi}\\right)\n", "\\end{math}" ], "text/plain": [ "(ta, rh, th, ph)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_hyp(p)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(p) on the 5-dimensional pseudo-Riemannian manifold R23\n" ] } ], "source": [ "q = Phi(p); print(q)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left({\\ell} \\cos\\left(\\frac{{\\tau}}{{\\ell}}\\right) \\cosh\\left({\\rho}\\right), {\\ell} \\cosh\\left({\\rho}\\right) \\sin\\left(\\frac{{\\tau}}{{\\ell}}\\right), {\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) \\sinh\\left({\\rho}\\right), {\\ell} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) \\sinh\\left({\\rho}\\right), {\\ell} \\cos\\left({\\theta}\\right) \\sinh\\left({\\rho}\\right)\\right)\n", "\\end{math}" ], "text/plain": [ "(l*cos(ta/l)*cosh(rh),\n", " l*cosh(rh)*sin(ta/l),\n", " l*cos(ph)*sin(th)*sinh(rh),\n", " l*sin(ph)*sin(th)*sinh(rh),\n", " l*cos(th)*sinh(rh))" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X23(q)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The image of $\\mathcal{M}$ by the immersion $\\Phi$ is a hyperboloid of one sheet, of equation $$-U^2-V^2+X^2+Y^2+Z^2=-\\ell^2.$$\n", "Indeed:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-{\\ell}^{2}\n", "\\end{math}" ], "text/plain": [ "-l^2" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(Uq,Vq,Xq,Yq,Zq) = X23(q)\n", "s = - Uq^2 - Vq^2 + Xq^2 + Yq^2 + Zq^2\n", "s.simplify_full()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may use the immersion $\\Phi$ to draw the coordinate grid $(\\tau,\\rho)$ in terms of the coordinates $(U,V,X)$ for $\\theta=\\pi/2$ and $\\phi=0$ ($X\\geq 0$ part) or $\\phi=\\pi$ \n", "($X\\leq 0$ part). The red (rep. grey) curves are those for which $\\rho={\\rm const}$ \n", "(resp. $\\tau={\\rm const}$):" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_hyp = X_hyp.plot(X23, mapping=Phi, ambient_coords=(V,X,U), fixed_coords={th:pi/2, ph:0}, \n", " ranges={ta:(0,2*pi), rh:(0,2)}, number_values=9, \n", " color={ta:'red', rh:'grey'}, thickness=2, parameters={l:1}, \n", " label_axes=False) # phi = 0 => X > 0 part\n", "graph_hyp += X_hyp.plot(X23, mapping=Phi, ambient_coords=(V,X,U), fixed_coords={th:pi/2, ph:pi},\n", " ranges={ta:(0,2*pi), rh:(0,2)}, number_values=9, \n", " color={ta:'red', rh:'grey'}, thickness=2, parameters={l:1}, \n", " label_axes=False) # phi = pi => X < 0 part\n", "show(graph_hyp, aspect_ratio=1, axes_labels=['V','X','U'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To have a nicer picture, we add the plot of the hyperboloid obtained by `parametric_plot` with $(\\tau,\\rho)$ as parameters and the expressions of $(U,V,X)$ in terms of $(\\tau,\\rho)$ deduced from the coordinate representation of $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left({\\ell} \\cos\\left(\\frac{{\\tau}}{{\\ell}}\\right) \\cosh\\left({\\rho}\\right), {\\ell} \\cosh\\left({\\rho}\\right) \\sin\\left(\\frac{{\\tau}}{{\\ell}}\\right), {\\ell} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) \\sinh\\left({\\rho}\\right), {\\ell} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) \\sinh\\left({\\rho}\\right), {\\ell} \\cos\\left({\\theta}\\right) \\sinh\\left({\\rho}\\right)\\right)\n", "\\end{math}" ], "text/plain": [ "Coordinate functions (l*cos(ta/l)*cosh(rh), l*cosh(rh)*sin(ta/l), l*cos(ph)*sin(th)*sinh(rh), l*sin(ph)*sin(th)*sinh(rh), l*cos(th)*sinh(rh)) on the Chart (M_0, (ta, rh, th, ph))" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.coord_functions() # the default pair of charts (X_hyp, X23) is assumed" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\cos\\left({\\tau}\\right) \\cosh\\left({\\rho}\\right), \\cosh\\left({\\rho}\\right) \\sin\\left({\\tau}\\right), \\sinh\\left({\\rho}\\right)\\right)\n", "\\end{math}" ], "text/plain": [ "(cos(ta)*cosh(rh), cosh(rh)*sin(ta), sinh(rh))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ug = Phi.coord_functions()[0](ta,rh,pi/2,0).subs({l:1}) # l=1 substituted to have numerical values\n", "Vg = Phi.coord_functions()[1](ta,rh,pi/2,0).subs({l:1})\n", "Xg = Phi.coord_functions()[2](ta,rh,pi/2,0).subs({l:1})\n", "Ug, Vg, Xg" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hyperboloid = parametric_plot3d([Vg, Xg, Ug], (ta,0,2*pi), (rh,-2,2), color=(1.,1.,0.9))\n", "graph_hyp += hyperboloid\n", "show(graph_hyp, aspect_ratio=1, axes_labels=['V','X','U'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spacetime metric" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As mentionned above, the AdS metric $g$ on $\\mathcal{M}$ is that induced by the flat metric $h$ on $\\mathbb{R}^{2,3}$, i.e.$g$ is the pullback of $h$ by the differentiable map $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "g = M.metric()\n", "g.set( Phi.pullback(h) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The expression of $g$ in terms of $\\mathcal{M}$'s default frame is found to be

" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = -\\cosh\\left({\\rho}\\right)^{2} \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} + {\\ell}^{2} \\mathrm{d} {\\rho}\\otimes \\mathrm{d} {\\rho} + {\\ell}^{2} \\sinh\\left({\\rho}\\right)^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + {\\ell}^{2} \\sin\\left({\\theta}\\right)^{2} \\sinh\\left({\\rho}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\n", "\\end{math}" ], "text/plain": [ "g = -cosh(rh)^2 dta*dta + l^2 drh*drh + l^2*sinh(rh)^2 dth*dth + l^2*sin(th)^2*sinh(rh)^2 dph*dph" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "-\\cosh\\left({\\rho}\\right)^{2} & 0 & 0 & 0 \\\\\n", "0 & {\\ell}^{2} & 0 & 0 \\\\\n", "0 & 0 & {\\ell}^{2} \\sinh\\left({\\rho}\\right)^{2} & 0 \\\\\n", "0 & 0 & 0 & {\\ell}^{2} \\sin\\left({\\theta}\\right)^{2} \\sinh\\left({\\rho}\\right)^{2}\n", "\\end{array}\\right)\n", "\\end{math}" ], "text/plain": [ "[ -cosh(rh)^2 0 0 0]\n", "[ 0 l^2 0 0]\n", "[ 0 0 l^2*sinh(rh)^2 0]\n", "[ 0 0 0 l^2*sin(th)^2*sinh(rh)^2]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Curvature

\n", "

The Riemann tensor of $g$ is

" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field Riem(g) of type (1,3) on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "Riem = g.riemann()\n", "print(Riem)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\tau}} \\, {\\rho} \\, {\\tau} \\, {\\rho} }^{ \\, {\\tau} \\phantom{\\, {\\rho}} \\phantom{\\, {\\tau}} \\phantom{\\, {\\rho}} } & = & -1 \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\tau}} \\, {\\theta} \\, {\\tau} \\, {\\theta} }^{ \\, {\\tau} \\phantom{\\, {\\theta}} \\phantom{\\, {\\tau}} \\phantom{\\, {\\theta}} } & = & -\\sinh\\left({\\rho}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\tau}} \\, {\\phi} \\, {\\tau} \\, {\\phi} }^{ \\, {\\tau} \\phantom{\\, {\\phi}} \\phantom{\\, {\\tau}} \\phantom{\\, {\\phi}} } & = & -\\sin\\left({\\theta}\\right)^{2} \\sinh\\left({\\rho}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\rho}} \\, {\\tau} \\, {\\tau} \\, {\\rho} }^{ \\, {\\rho} \\phantom{\\, {\\tau}} \\phantom{\\, {\\tau}} \\phantom{\\, {\\rho}} } & = & -\\frac{\\cosh\\left({\\rho}\\right)^{2}}{{\\ell}^{2}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\rho}} \\, {\\theta} \\, {\\rho} \\, {\\theta} }^{ \\, {\\rho} \\phantom{\\, {\\theta}} \\phantom{\\, {\\rho}} \\phantom{\\, {\\theta}} } & = & -\\sinh\\left({\\rho}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\rho}} \\, {\\phi} \\, {\\rho} \\, {\\phi} }^{ \\, {\\rho} \\phantom{\\, {\\phi}} \\phantom{\\, {\\rho}} \\phantom{\\, {\\phi}} } & = & -\\sin\\left({\\theta}\\right)^{2} \\sinh\\left({\\rho}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\tau} \\, {\\tau} \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, {\\tau}} \\phantom{\\, {\\tau}} \\phantom{\\, {\\theta}} } & = & -\\frac{\\cosh\\left({\\rho}\\right)^{2}}{{\\ell}^{2}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\rho} \\, {\\rho} \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, {\\rho}} \\phantom{\\, {\\rho}} \\phantom{\\, {\\theta}} } & = & 1 \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\theta} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & -\\sin\\left({\\theta}\\right)^{2} \\sinh\\left({\\rho}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\tau} \\, {\\tau} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\tau}} \\phantom{\\, {\\tau}} \\phantom{\\, {\\phi}} } & = & -\\frac{\\cosh\\left({\\rho}\\right)^{2}}{{\\ell}^{2}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\rho} \\, {\\rho} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\rho}} \\phantom{\\, {\\rho}} \\phantom{\\, {\\phi}} } & = & 1 \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\sinh\\left({\\rho}\\right)^{2} \\end{array}\n", "\\end{math}" ], "text/plain": [ "Riem(g)^ta_rh,ta,rh = -1 \n", "Riem(g)^ta_th,ta,th = -sinh(rh)^2 \n", "Riem(g)^ta_ph,ta,ph = -sin(th)^2*sinh(rh)^2 \n", "Riem(g)^rh_ta,ta,rh = -cosh(rh)^2/l^2 \n", "Riem(g)^rh_th,rh,th = -sinh(rh)^2 \n", "Riem(g)^rh_ph,rh,ph = -sin(th)^2*sinh(rh)^2 \n", "Riem(g)^th_ta,ta,th = -cosh(rh)^2/l^2 \n", "Riem(g)^th_rh,rh,th = 1 \n", "Riem(g)^th_ph,th,ph = -sin(th)^2*sinh(rh)^2 \n", "Riem(g)^ph_ta,ta,ph = -cosh(rh)^2/l^2 \n", "Riem(g)^ph_rh,rh,ph = 1 \n", "Riem(g)^ph_th,th,ph = sinh(rh)^2 " ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp(only_nonredundant=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Ricci tensor:

" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field of symmetric bilinear forms Ric(g) on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(g\\right) = \\frac{3 \\, \\cosh\\left({\\rho}\\right)^{2}}{{\\ell}^{2}} \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} -3 \\mathrm{d} {\\rho}\\otimes \\mathrm{d} {\\rho} -3 \\, \\sinh\\left({\\rho}\\right)^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} -3 \\, \\sin\\left({\\theta}\\right)^{2} \\sinh\\left({\\rho}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\n", "\\end{math}" ], "text/plain": [ "Ric(g) = 3*cosh(rh)^2/l^2 dta*dta - 3 drh*drh - 3*sinh(rh)^2 dth*dth - 3*sin(th)^2*sinh(rh)^2 dph*dph" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "print(Ric)\n", "Ric.display()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{3 \\, \\cosh\\left({\\rho}\\right)^{2}}{{\\ell}^{2}} & 0 & 0 & 0 \\\\\n", "0 & -3 & 0 & 0 \\\\\n", "0 & 0 & -3 \\, \\sinh\\left({\\rho}\\right)^{2} & 0 \\\\\n", "0 & 0 & 0 & -3 \\, \\sin\\left({\\theta}\\right)^{2} \\sinh\\left({\\rho}\\right)^{2}\n", "\\end{array}\\right)\n", "\\end{math}" ], "text/plain": [ "[ 3*cosh(rh)^2/l^2 0 0 0]\n", "[ 0 -3 0 0]\n", "[ 0 0 -3*sinh(rh)^2 0]\n", "[ 0 0 0 -3*sin(th)^2*sinh(rh)^2]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Ricci scalar:

" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field r(g) on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\mathrm{r}\\left(g\\right):& \\mathcal{M} & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ \\mathcal{M}_0 : & \\left({\\tau}, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{12}{{\\ell}^{2}} \\end{array}\n", "\\end{math}" ], "text/plain": [ "r(g): M --> R\n", "on M_0: (ta, rh, th, ph) |--> -12/l^2" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = g.ricci_scalar()\n", "print(R)\n", "R.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We recover the fact that AdS spacetime has a constant curvature. It is indeed a **maximally symmetric space**. In particular, the Riemann tensor is expressible as\n", "$$ R^i_{\\ \\, jlk} = \\frac{R}{n(n-1)} \\left( \\delta^i_{\\ \\, k} g_{jl} - \\delta^i_{\\ \\, l} g_{jk} \\right), $$\n", "where $n$ is the dimension of $\\mathcal{M}$: $n=4$ in the present case. Let us check this formula here, under the form $R^i_{\\ \\, jlk} = -\\frac{R}{6} g_{j[k} \\delta^i_{\\ \\, l]}$:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\n", "\\end{math}" ], "text/plain": [ "True" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = M.tangent_identity_field() \n", "Riem == - (R/6)*(g*delta).antisymmetrize(2,3) # 2,3 = last positions of the \n", " # type-(1,3) tensor g*delta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may also check that AdS metric is a solution of the vacuum **Einstein equation** with (negative) cosmological constant $\\Lambda = - 3/\\ell^2$:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\n", "\\end{math}" ], "text/plain": [ "True" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Lambda = -3/l^2\n", "Ric - 1/2*R*g + Lambda*g == 0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Radial null geodesics\n", "\n", "Null geodesics that are radial with respect to coordinates $(\\tau,\\rho,\\theta,\\phi)$ obey\n", "$$ \\tau = \\pm 2 \\ell \\left( \\mathrm{atan} \\left(\\mathrm{e}^\\rho\\right) - \\frac{\\pi}{4} \\right) + \\tau_0,$$\n", "where $\\tau_0$ is a constant (the value of $\\tau$ at $\\rho=0$). Note that, due to the homogeneity of AdS spacetime, any null geodesic is a \"radial\" geodesic with respect to some coordinate system $(\\tau',\\rho',\\theta',\\phi')$, as in Minkowski spacetime, any null geodesic is a straight line and one can always find a Minkowskian coordinate system $(t',x',y',z')$ with respect to which the null geodesic is radial.\n", "\n", "Let us consider two finite families of radial null geodesics having $\\theta=\\pi/2$ and $\\phi=0$ or $\\pi$: \n", "- `null_geod1` has $\\phi=\\pi$ when $\\tau< 0$ and $\\phi=0$ when $\\tau>0$\n", "- `null_geod2` has $\\phi=0$ when $\\tau<0$ and $\\phi=\\pi$ when $\\tau>0$" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "lamb = var('lamb', latex_name=r'\\lambda')\n", "null_geod1 = [M.curve({X_hyp: [2*sgn(lamb)*l*(atan(exp(abs(lamb))) - pi/4) + 2*pi*(i-4)/8, \n", " abs(lamb), pi/2, pi*unit_step(-lamb)]}, \n", " (lamb, -oo, +oo)) for i in range(9)]\n", "null_geod2 = [M.curve({X_hyp: [2*sgn(lamb)*l*(atan(exp(abs(lamb))) - pi/4) + 2*pi*(i-4)/8, \n", " abs(lamb), pi/2, pi*unit_step(lamb)]}, \n", " (lamb, -oo, +oo)) for i in range(9)]\n", "null_geods = null_geod1 + null_geod2" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Curve in the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "print(null_geods[0])" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\Bold{R} & \\longrightarrow & \\mathcal{M} \\\\ & {\\lambda} & \\longmapsto & \\left({\\tau}, {\\rho}, {\\theta}, {\\phi}\\right) = \\left(-\\pi - \\frac{1}{2} \\, {\\left(\\pi - 4 \\, \\arctan\\left(e^{\\left({\\left| {\\lambda} \\right|}\\right)}\\right)\\right)} {\\ell} \\mathrm{sgn}\\left({\\lambda}\\right), {\\left| {\\lambda} \\right|}, \\frac{1}{2} \\, \\pi, \\pi \\mathrm{u}\\left(-{\\lambda}\\right)\\right) \\end{array}\n", "\\end{math}" ], "text/plain": [ "R --> M\n", " lamb |--> (ta, rh, th, ph) = (-pi - 1/2*(pi - 4*arctan(e^abs(lamb)))*l*sgn(lamb), abs(lamb), 1/2*pi, pi*unit_step(-lamb))" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "null_geods[0].display()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\Bold{R} & \\longrightarrow & \\mathcal{M} \\\\ & {\\lambda} & \\longmapsto & \\left({\\tau}, {\\rho}, {\\theta}, {\\phi}\\right) = \\left(-\\pi - \\frac{1}{2} \\, {\\left(\\pi - 4 \\, \\arctan\\left(e^{\\left({\\left| {\\lambda} \\right|}\\right)}\\right)\\right)} {\\ell} \\mathrm{sgn}\\left({\\lambda}\\right), {\\left| {\\lambda} \\right|}, \\frac{1}{2} \\, \\pi, \\pi \\mathrm{u}\\left({\\lambda}\\right)\\right) \\end{array}\n", "\\end{math}" ], "text/plain": [ "R --> M\n", " lamb |--> (ta, rh, th, ph) = (-pi - 1/2*(pi - 4*arctan(e^abs(lamb)))*l*sgn(lamb), abs(lamb), 1/2*pi, pi*unit_step(lamb))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "null_geods[9].display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To graphically display these geodesics, we introduce a Cartesian-like coordinate system\n", "$(\\tau,x_\\rho,y_\\rho,z_\\rho)$ linked to $(\\tau,\\rho,\\theta,\\phi)$ by the standard formulas:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & {\\tau} \\\\ {x_\\rho} & = & {\\rho} \\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) \\\\ {y_\\rho} & = & {\\rho} \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right) \\\\ {z_\\rho} & = & {\\rho} \\cos\\left({\\theta}\\right) \\end{array}\\right.\n", "\\end{math}" ], "text/plain": [ "ta = ta\n", "x_rho = rh*cos(ph)*sin(th)\n", "y_rho = rh*sin(ph)*sin(th)\n", "z_rho = rh*cos(th)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_hyp_graph. = M0.chart(r'ta:\\tau x_rho:x_\\rho y_rho:y_\\rho z_rho:z_\\rho')\n", "hyp_to_hyp_graph = X_hyp.transition_map(X_hyp_graph, [ta, rh*sin(th)*cos(ph), \n", " rh*sin(th)*sin(ph), rh*cos(th)])\n", "hyp_to_hyp_graph.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us plot the null geodesics in terms of the coordinates $(\\tau,x_\\rho)$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 36 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_2d = Graphics()\n", "for geod in null_geods:\n", " geod.expr(geod.domain().canonical_chart(), X_hyp_graph)\n", " graph_2d += geod.plot(X_hyp_graph, ambient_coords=(x_rho,ta), prange=(-4,4),\n", " parameters={l:1}, color='green', thickness=1.5)\n", "graph_2d += X_hyp_graph.plot(X_hyp_graph, ambient_coords=(x_rho,ta), \n", " fixed_coords={th:0, ph:pi}, \n", " ranges={ta:(-pi,pi), x_rho:(-4,4)}, \n", " number_values={ta: 9, x_rho: 9},\n", " color={ta:'red', x_rho:'grey'}, parameters={l:1})\n", "show(graph_2d, aspect_ratio=1, ymin=-pi, ymax=pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also get a 3D view of the radial null geodesics via the isometric immersion $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "