{ "cells": [ { "cell_type": "markdown", "id": "814b300d", "metadata": {}, "source": [ "# NHEK spacetime\n", "\n", "This This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://luth.obspm.fr/~luthier/gourgoulhon/bh16/).\n", "It explores the global Near-Horizon Extremal Kerr (NHEK) spacetime $(\\mathcal{N}, h)$. " ] }, { "cell_type": "markdown", "id": "66a7d177", "metadata": {}, "source": [ "This notebook requires a version of SageMath at least equal to 9.0:" ] }, { "cell_type": "code", "execution_count": 1, "id": "f9de8307", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.5.beta2, Release Date: 2021-09-26'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "id": "524201e9", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX rendering, and, to speed up computations, we ask for running them in parallel on 8 threads:" ] }, { "cell_type": "code", "execution_count": 2, "id": "0336e42f", "metadata": {}, "outputs": [], "source": [ "%display latex\n", "Parallelism().set(nproc=8)" ] }, { "cell_type": "markdown", "id": "1fca1efe", "metadata": {}, "source": [ "## Manifold" ] }, { "cell_type": "code", "execution_count": 3, "id": "31a95435", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional Lorentzian manifold N\n" ] } ], "source": [ "N = Manifold(4, 'N', latex_name=r'\\mathscr{N}', structure='Lorentzian',\n", " metric_name='h')\n", "print(N)" ] }, { "cell_type": "markdown", "id": "47e15390", "metadata": {}, "source": [ "Global coordinate chart $(\\tau, y, \\theta, \\psi)$:" ] }, { "cell_type": "code", "execution_count": 4, "id": "d8bc6942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (N, (ta, y, th, ps))\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N},({\\tau}, y, {\\theta}, {\\psi})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N},({\\tau}, y, {\\theta}, {\\psi})\\right)$$" ], "text/plain": [ "Chart (N, (ta, y, th, ps))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X. = N.chart(r\"ta:\\tau y th:(0,pi):\\theta ps:(0,2*pi):periodic:\\psi\") \n", "print(X)\n", "X" ] }, { "cell_type": "code", "execution_count": 5, "id": "f7362539", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad y :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\psi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad y :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\psi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}$$" ], "text/plain": [ "ta: (-oo, +oo); y: (-oo, +oo); th: (0, pi); ps: [0, 2*pi] (periodic)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X.coord_range()" ] }, { "cell_type": "markdown", "id": "f1e5559e", "metadata": {}, "source": [ "The coordinate 1-forms:" ] }, { "cell_type": "code", "execution_count": 6, "id": "6b9dfb60", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathrm{d} {\\tau}, \\mathrm{d} y, \\mathrm{d} {\\theta}, \\mathrm{d} {\\psi}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathrm{d} {\\tau}, \\mathrm{d} y, \\mathrm{d} {\\theta}, \\mathrm{d} {\\psi}\\right)$$" ], "text/plain": [ "(1-form dta on the 4-dimensional Lorentzian manifold N,\n", " 1-form dy on the 4-dimensional Lorentzian manifold N,\n", " 1-form dth on the 4-dimensional Lorentzian manifold N,\n", " 1-form dps on the 4-dimensional Lorentzian manifold N)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X.coframe()[:]" ] }, { "cell_type": "code", "execution_count": 7, "id": "1d298d03", "metadata": {}, "outputs": [], "source": [ "dta, dy, dth, dps = X.coframe()[:]" ] }, { "cell_type": "markdown", "id": "666bda72", "metadata": {}, "source": [ "## NHEK metric" ] }, { "cell_type": "markdown", "id": "a5ad1c3c", "metadata": {}, "source": [ "The mass parameter $m$ appears in the the NHEK metric $h$ as an overall scale parameter $m^2$. In what follows, we set $m=1$ for simplicity. We then declare $h$ as" ] }, { "cell_type": "code", "execution_count": 8, "id": "bca48703", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = \\left( -\\frac{\\sin\\left({\\theta}\\right)^{4} + {\\left(\\sin\\left({\\theta}\\right)^{4} - 8 \\, \\sin\\left({\\theta}\\right)^{2} + 4\\right)} y^{2} - 4 \\, \\sin\\left({\\theta}\\right)^{2} + 4}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, y \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\psi} + \\left( \\frac{\\cos\\left({\\theta}\\right)^{2} + 1}{y^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y + \\left( \\cos\\left({\\theta}\\right)^{2} + 1 \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{4 \\, y \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\psi}\\otimes \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\psi}\\otimes \\mathrm{d} {\\psi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = \\left( -\\frac{\\sin\\left({\\theta}\\right)^{4} + {\\left(\\sin\\left({\\theta}\\right)^{4} - 8 \\, \\sin\\left({\\theta}\\right)^{2} + 4\\right)} y^{2} - 4 \\, \\sin\\left({\\theta}\\right)^{2} + 4}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, y \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\psi} + \\left( \\frac{\\cos\\left({\\theta}\\right)^{2} + 1}{y^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y + \\left( \\cos\\left({\\theta}\\right)^{2} + 1 \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{4 \\, y \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\psi}\\otimes \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\psi}\\otimes \\mathrm{d} {\\psi}$$" ], "text/plain": [ "h = -(sin(th)^4 + (sin(th)^4 - 8*sin(th)^2 + 4)*y^2 - 4*sin(th)^2 + 4)/(cos(th)^2 + 1) dta⊗dta + 4*y*sin(th)^2/(cos(th)^2 + 1) dta⊗dps + (cos(th)^2 + 1)/(y^2 + 1) dy⊗dy + (cos(th)^2 + 1) dth⊗dth + 4*y*sin(th)^2/(cos(th)^2 + 1) dps⊗dta + 4*sin(th)^2/(cos(th)^2 + 1) dps⊗dps" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = N.metric()\n", "dps_ydta = dps + y*dta\n", "h.set((1 + cos(th)^2)*(- (1 + y^2)*(dta*dta)+ (dy*dy)/(1 + y^2) + dth*dth)\n", " + 4*sin(th)^2/(1 + cos(th)^2)*(dps_ydta*dps_ydta))\n", "h.display()" ] }, { "cell_type": "markdown", "id": "12b24629", "metadata": {}, "source": [ "The NHEK metric is a solution of the **vacuum Einstein equation**:" ] }, { "cell_type": "code", "execution_count": 9, "id": "1ae5d6d8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(h\\right) = 0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(h\\right) = 0$$" ], "text/plain": [ "Ric(h) = 0" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.ricci().display()" ] }, { "cell_type": "markdown", "id": "a872c71a", "metadata": {}, "source": [ "### Inverse metric" ] }, { "cell_type": "code", "execution_count": 10, "id": "e33b2d58", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{\\sin\\left({\\theta}\\right)^{2} - 2}{\\cos\\left({\\theta}\\right)^{4} + {\\left(\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1\\right)} y^{2} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 & \\frac{y}{{\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} y^{2} + \\cos\\left({\\theta}\\right)^{2} + 1} \\\\\n", "0 & \\frac{y^{2} + 1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 \\\\\n", "0 & 0 & \\frac{1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 \\\\\n", "\\frac{y}{{\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} y^{2} + \\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 & \\frac{\\cos\\left({\\theta}\\right)^{6} + 3 \\, \\cos\\left({\\theta}\\right)^{4} + {\\left(\\cos\\left({\\theta}\\right)^{6} + 7 \\, \\cos\\left({\\theta}\\right)^{4} + 3 \\, \\cos\\left({\\theta}\\right)^{2} - 3\\right)} y^{2} + 3 \\, \\cos\\left({\\theta}\\right)^{2} + 1}{4 \\, {\\left(\\sin\\left({\\theta}\\right)^{6} - 4 \\, \\sin\\left({\\theta}\\right)^{4} + {\\left(\\sin\\left({\\theta}\\right)^{6} - 4 \\, \\sin\\left({\\theta}\\right)^{4} + 4 \\, \\sin\\left({\\theta}\\right)^{2}\\right)} y^{2} + 4 \\, \\sin\\left({\\theta}\\right)^{2}\\right)}}\n", "\\end{array}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{\\sin\\left({\\theta}\\right)^{2} - 2}{\\cos\\left({\\theta}\\right)^{4} + {\\left(\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1\\right)} y^{2} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 & \\frac{y}{{\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} y^{2} + \\cos\\left({\\theta}\\right)^{2} + 1} \\\\\n", "0 & \\frac{y^{2} + 1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 \\\\\n", "0 & 0 & \\frac{1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 \\\\\n", "\\frac{y}{{\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} y^{2} + \\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 & \\frac{\\cos\\left({\\theta}\\right)^{6} + 3 \\, \\cos\\left({\\theta}\\right)^{4} + {\\left(\\cos\\left({\\theta}\\right)^{6} + 7 \\, \\cos\\left({\\theta}\\right)^{4} + 3 \\, \\cos\\left({\\theta}\\right)^{2} - 3\\right)} y^{2} + 3 \\, \\cos\\left({\\theta}\\right)^{2} + 1}{4 \\, {\\left(\\sin\\left({\\theta}\\right)^{6} - 4 \\, \\sin\\left({\\theta}\\right)^{4} + {\\left(\\sin\\left({\\theta}\\right)^{6} - 4 \\, \\sin\\left({\\theta}\\right)^{4} + 4 \\, \\sin\\left({\\theta}\\right)^{2}\\right)} y^{2} + 4 \\, \\sin\\left({\\theta}\\right)^{2}\\right)}}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ (sin(th)^2 - 2)/(cos(th)^4 + (cos(th)^4 + 2*cos(th)^2 + 1)*y^2 + 2*cos(th)^2 + 1) 0 0 y/((cos(th)^2 + 1)*y^2 + cos(th)^2 + 1)]\n", "[ 0 (y^2 + 1)/(cos(th)^2 + 1) 0 0]\n", "[ 0 0 1/(cos(th)^2 + 1) 0]\n", "[ y/((cos(th)^2 + 1)*y^2 + cos(th)^2 + 1) 0 0 1/4*(cos(th)^6 + 3*cos(th)^4 + (cos(th)^6 + 7*cos(th)^4 + 3*cos(th)^2 - 3)*y^2 + 3*cos(th)^2 + 1)/(sin(th)^6 - 4*sin(th)^4 + (sin(th)^6 - 4*sin(th)^4 + 4*sin(th)^2)*y^2 + 4*sin(th)^2)]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.inverse()[:]" ] }, { "cell_type": "markdown", "id": "72c48a47", "metadata": {}, "source": [ "Some simplifications are in order:" ] }, { "cell_type": "code", "execution_count": 11, "id": "230acd21", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{\\sin\\left({\\theta}\\right)^{2} - 2}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}^{2}} & 0 & 0 & \\frac{y}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} \\\\\n", "0 & \\frac{y^{2} + 1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 \\\\\n", "0 & 0 & \\frac{1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 \\\\\n", "\\frac{y}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} & 0 & 0 & \\frac{{\\left(y^{2} \\cos\\left({\\theta}\\right)^{4} + 6 \\, y^{2} \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\theta}\\right)^{4} - 3 \\, y^{2} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}}{4 \\, {\\left(y^{2} + 1\\right)} {\\left(\\sin\\left({\\theta}\\right)^{2} - 2\\right)}^{2} \\sin\\left({\\theta}\\right)^{2}}\n", "\\end{array}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{\\sin\\left({\\theta}\\right)^{2} - 2}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}^{2}} & 0 & 0 & \\frac{y}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} \\\\\n", "0 & \\frac{y^{2} + 1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 \\\\\n", "0 & 0 & \\frac{1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 \\\\\n", "\\frac{y}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} & 0 & 0 & \\frac{{\\left(y^{2} \\cos\\left({\\theta}\\right)^{4} + 6 \\, y^{2} \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\theta}\\right)^{4} - 3 \\, y^{2} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}}{4 \\, {\\left(y^{2} + 1\\right)} {\\left(\\sin\\left({\\theta}\\right)^{2} - 2\\right)}^{2} \\sin\\left({\\theta}\\right)^{2}}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ (sin(th)^2 - 2)/((y^2 + 1)*(cos(th)^2 + 1)^2) 0 0 y/((y^2 + 1)*(cos(th)^2 + 1))]\n", "[ 0 (y^2 + 1)/(cos(th)^2 + 1) 0 0]\n", "[ 0 0 1/(cos(th)^2 + 1) 0]\n", "[ y/((y^2 + 1)*(cos(th)^2 + 1)) 0 0 1/4*(y^2*cos(th)^4 + 6*y^2*cos(th)^2 + cos(th)^4 - 3*y^2 + 2*cos(th)^2 + 1)*(cos(th)^2 + 1)/((y^2 + 1)*(sin(th)^2 - 2)^2*sin(th)^2)]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.inverse().apply_map(factor)\n", "h.inverse()[:]" ] }, { "cell_type": "code", "execution_count": 12, "id": "6c57700f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{1}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{1}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}}$$" ], "text/plain": [ "-1/((y^2 + 1)*(cos(th)^2 + 1))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h00 = h.inverse()[0,0].expr().subs({sin(th)^2: 1 - cos(th)^2})\n", "h00" ] }, { "cell_type": "code", "execution_count": 13, "id": "e8d61828", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{y^{2} \\cos\\left({\\theta}\\right)^{4} + 6 \\, y^{2} \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\theta}\\right)^{4} - 3 \\, y^{2} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1}{4 \\, {\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} \\sin\\left({\\theta}\\right)^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{y^{2} \\cos\\left({\\theta}\\right)^{4} + 6 \\, y^{2} \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\theta}\\right)^{4} - 3 \\, y^{2} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1}{4 \\, {\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} \\sin\\left({\\theta}\\right)^{2}}$$" ], "text/plain": [ "1/4*(y^2*cos(th)^4 + 6*y^2*cos(th)^2 + cos(th)^4 - 3*y^2 + 2*cos(th)^2 + 1)/((y^2 + 1)*(cos(th)^2 + 1)*sin(th)^2)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h33 = h.inverse()[3,3].expr().subs({sin(th)^2: 1 - cos(th)^2})\n", "h33" ] }, { "cell_type": "markdown", "id": "42aac135", "metadata": {}, "source": [ "Hence we set:" ] }, { "cell_type": "code", "execution_count": 14, "id": "c026559d", "metadata": {}, "outputs": [], "source": [ "h.inverse()[0,0] = h00\n", "h.inverse()[3,3] = h33" ] }, { "cell_type": "markdown", "id": "d6657b61", "metadata": {}, "source": [ "and we get" ] }, { "cell_type": "code", "execution_count": 15, "id": "3436cd8d", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "-\\frac{1}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} & 0 & 0 & \\frac{y}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} \\\\\n", "0 & \\frac{y^{2} + 1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 \\\\\n", "0 & 0 & \\frac{1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 \\\\\n", "\\frac{y}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} & 0 & 0 & \\frac{y^{2} \\cos\\left({\\theta}\\right)^{4} + 6 \\, y^{2} \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\theta}\\right)^{4} - 3 \\, y^{2} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1}{4 \\, {\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} \\sin\\left({\\theta}\\right)^{2}}\n", "\\end{array}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "-\\frac{1}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} & 0 & 0 & \\frac{y}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} \\\\\n", "0 & \\frac{y^{2} + 1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 & 0 \\\\\n", "0 & 0 & \\frac{1}{\\cos\\left({\\theta}\\right)^{2} + 1} & 0 \\\\\n", "\\frac{y}{{\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}} & 0 & 0 & \\frac{y^{2} \\cos\\left({\\theta}\\right)^{4} + 6 \\, y^{2} \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\theta}\\right)^{4} - 3 \\, y^{2} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1}{4 \\, {\\left(y^{2} + 1\\right)} {\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} \\sin\\left({\\theta}\\right)^{2}}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ -1/((y^2 + 1)*(cos(th)^2 + 1)) 0 0 y/((y^2 + 1)*(cos(th)^2 + 1))]\n", "[ 0 (y^2 + 1)/(cos(th)^2 + 1) 0 0]\n", "[ 0 0 1/(cos(th)^2 + 1) 0]\n", "[ y/((y^2 + 1)*(cos(th)^2 + 1)) 0 0 1/4*(y^2*cos(th)^4 + 6*y^2*cos(th)^2 + cos(th)^4 - 3*y^2 + 2*cos(th)^2 + 1)/((y^2 + 1)*(cos(th)^2 + 1)*sin(th)^2)]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.inverse()[:]" ] }, { "cell_type": "markdown", "id": "b2279570", "metadata": {}, "source": [ "## Killing vectors" ] }, { "cell_type": "markdown", "id": "b9b30cc4", "metadata": {}, "source": [ "Two obvious Killing vectors are $\\partial/\\partial\\psi$ and $\\partial/\\partial\\tau$, since the components of $h$ do not depend on $\\psi$ or $\\tau$:" ] }, { "cell_type": "code", "execution_count": 16, "id": "78b4e47e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\eta = \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\eta = \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "eta = ∂/∂ps" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eta = N.vector_field(0, 0, 0, 1, name='eta', latex_name=r'\\eta')\n", "eta.display()" ] }, { "cell_type": "code", "execution_count": 17, "id": "7c67502e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.lie_derivative(eta).display()" ] }, { "cell_type": "code", "execution_count": 18, "id": "602eb9d8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_0 = \\frac{\\partial}{\\partial {\\tau} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_0 = \\frac{\\partial}{\\partial {\\tau} }$$" ], "text/plain": [ "J_0 = ∂/∂ta" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "J0 = N.vector_field(1, 0, 0, 0, name='J_0')\n", "J0.display()" ] }, { "cell_type": "code", "execution_count": 19, "id": "5fbe1b7e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.lie_derivative(J0).display()" ] }, { "cell_type": "markdown", "id": "7b6ead86", "metadata": {}, "source": [ "A third Killing vector arises from the isometry expressed by $(T,R)\\mapsto(\\alpha T, R/\\alpha)$ in Poincaré-type coordinates:" ] }, { "cell_type": "code", "execution_count": 20, "id": "0b1ddb03", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_1 = \\left( \\frac{y \\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -\\sqrt{y^{2} + 1} \\cos\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_1 = \\left( \\frac{y \\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -\\sqrt{y^{2} + 1} \\cos\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "J_1 = y*sin(ta)/sqrt(y^2 + 1) ∂/∂ta - sqrt(y^2 + 1)*cos(ta) ∂/∂y + sin(ta)/sqrt(y^2 + 1) ∂/∂ps" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "J1 = N.vector_field(y*sin(ta)/sqrt(1 + y^2), -cos(ta)*sqrt(1 + y^2),\n", " 0, sin(ta)/sqrt(1 + y^2), name='J_1')\n", "J1.display() " ] }, { "cell_type": "code", "execution_count": 21, "id": "7935aa5e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.lie_derivative(J1).display()" ] }, { "cell_type": "markdown", "id": "09e2c7c9", "metadata": {}, "source": [ "Finally a fourth Killing vector is $\\partial/\\partial T$ of the Poincaré-type coordinates. We actually consider\n", "the linear combination $\\partial/\\partial T - \\partial/\\partial\\tau$ since it has slightly simpler components\n", "in terms of the global coordinates $(\\tau,y,\\theta,\\psi)$:" ] }, { "cell_type": "code", "execution_count": 22, "id": "e42911a0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_2 = \\left( \\frac{y \\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( \\sqrt{y^{2} + 1} \\sin\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_2 = \\left( \\frac{y \\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( \\sqrt{y^{2} + 1} \\sin\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "J_2 = y*cos(ta)/sqrt(y^2 + 1) ∂/∂ta + sqrt(y^2 + 1)*sin(ta) ∂/∂y + cos(ta)/sqrt(y^2 + 1) ∂/∂ps" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "J2 = N.vector_field(y*cos(ta)/sqrt(1 + y^2), sin(ta)*sqrt(1 + y^2),\n", " 0, cos(ta)/sqrt(1 + y^2), name='J_2')\n", "J2.display() " ] }, { "cell_type": "code", "execution_count": 23, "id": "3350e12f", "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": [ "h.lie_derivative(J2).display()" ] }, { "cell_type": "markdown", "id": "e53cf555", "metadata": {}, "source": [ "### Commutation relations\n", "\n", "First of all we notice that $\\eta$ commutes with all the three other Killing vectors:" ] }, { "cell_type": "code", "execution_count": 24, "id": "321b44cc", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[\\eta,J_0\\right] = 0, \\left[\\eta,J_1\\right] = 0, \\left[\\eta,J_2\\right] = 0\\right]\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[\\eta,J_0\\right] = 0, \\left[\\eta,J_1\\right] = 0, \\left[\\eta,J_2\\right] = 0\\right]$$" ], "text/plain": [ "[[eta,J_0] = 0, [eta,J_1] = 0, [eta,J_2] = 0]" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[eta.bracket(j).display() for j in (J0, J1, J2)]" ] }, { "cell_type": "markdown", "id": "3f463b0e", "metadata": {}, "source": [ "To write easily the other commutation relations, we supplement $(J_0, J_1, J_2)$ by $\\partial/\\partial\\theta$ to make it a vector frame on $\\mathscr{N}$:" ] }, { "cell_type": "code", "execution_count": 25, "id": "55d8b66c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N}, \\left(J_{0},J_{1},J_{2},J_{3}\\right)\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N}, \\left(J_{0},J_{1},J_{2},J_{3}\\right)\\right)$$" ], "text/plain": [ "Vector frame (N, (J_0,J_1,J_2,J_3))" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "J = N.vector_frame('J', (J0, J1, J2, X.frame()[2]))\n", "J0, J1, J2 = J[:-1]\n", "J" ] }, { "cell_type": "code", "execution_count": 26, "id": "533ba689", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{2} = J_{2}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{2} = J_{2}$$" ], "text/plain": [ "J_2 = J_2" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "J2.display(J)" ] }, { "cell_type": "code", "execution_count": 27, "id": "55bcd369", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{0} = \\frac{\\partial}{\\partial {\\tau} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{0} = \\frac{\\partial}{\\partial {\\tau} }$$" ], "text/plain": [ "J_0 = ∂/∂ta" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{1} = \\left( \\frac{y \\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -\\sqrt{y^{2} + 1} \\cos\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{1} = \\left( \\frac{y \\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -\\sqrt{y^{2} + 1} \\cos\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "J_1 = y*sin(ta)/sqrt(y^2 + 1) ∂/∂ta - sqrt(y^2 + 1)*cos(ta) ∂/∂y + sin(ta)/sqrt(y^2 + 1) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{2} = \\left( \\frac{y \\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( \\sqrt{y^{2} + 1} \\sin\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{2} = \\left( \\frac{y \\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( \\sqrt{y^{2} + 1} \\sin\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "J_2 = y*cos(ta)/sqrt(y^2 + 1) ∂/∂ta + sqrt(y^2 + 1)*sin(ta) ∂/∂y + cos(ta)/sqrt(y^2 + 1) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{3} = \\frac{\\partial}{\\partial {\\theta} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{3} = \\frac{\\partial}{\\partial {\\theta} }$$" ], "text/plain": [ "J_3 = ∂/∂th" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for v in J:\n", " show(v.display())" ] }, { "cell_type": "markdown", "id": "26779a05", "metadata": {}, "source": [ "Then we ask for the display of the commutators in that frame:" ] }, { "cell_type": "code", "execution_count": 28, "id": "174899f8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[J_{0},J_{1}\\right] = J_{2}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[J_{0},J_{1}\\right] = J_{2}$$" ], "text/plain": [ "[J_0,J_1] = J_2" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "J0.bracket(J1).display(J)" ] }, { "cell_type": "code", "execution_count": 29, "id": "15e82bfc", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[J_{0},J_{2}\\right] = -J_{1}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[J_{0},J_{2}\\right] = -J_{1}$$" ], "text/plain": [ "[J_0,J_2] = -J_1" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "J0.bracket(J2).display(J)" ] }, { "cell_type": "code", "execution_count": 30, "id": "44623dc1", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[J_{1},J_{2}\\right] = -J_{0}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[J_{1},J_{2}\\right] = -J_{0}$$" ], "text/plain": [ "[J_1,J_2] = -J_0" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "J1.bracket(J2).display(J)" ] }, { "cell_type": "markdown", "id": "40a9423d", "metadata": {}, "source": [ "These commutation relations are not the standard ones for $\\mathfrak{sl}(2,\\mathbb{R})$; in order to get these, let us introduce the following linear combinations:" ] }, { "cell_type": "code", "execution_count": 31, "id": "45e95a38", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_0 = 2 J_{1}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_0 = 2 J_{1}$$" ], "text/plain": [ "K_0 = 2 J_1" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K0 = 2*J1\n", "K0.set_name('K_0')\n", "K0.display(J)" ] }, { "cell_type": "code", "execution_count": 32, "id": "377037f7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_1 = -J_{0}+J_{2}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_1 = -J_{0}+J_{2}$$" ], "text/plain": [ "K_1 = -J_0 + J_2" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K1 = J2 - J0\n", "K1.set_name('K_1')\n", "K1.display(J)" ] }, { "cell_type": "code", "execution_count": 33, "id": "79c85b3f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_2 = J_{0}+J_{2}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_2 = J_{0}+J_{2}$$" ], "text/plain": [ "K_2 = J_0 + J_2" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K2 = J2 + J0\n", "K2.set_name('K_2')\n", "K2.display(J)" ] }, { "cell_type": "code", "execution_count": 34, "id": "c364206d", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N}, \\left(K_{0},K_{1},K_{2},K_{3}\\right)\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N}, \\left(K_{0},K_{1},K_{2},K_{3}\\right)\\right)$$" ], "text/plain": [ "Vector frame (N, (K_0,K_1,K_2,K_3))" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K = N.vector_frame('K', (K0, K1, K2, X.frame()[2]))\n", "K0, K1, K2 = K[:-1]\n", "K" ] }, { "cell_type": "code", "execution_count": 35, "id": "4b1e4121", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{0} = \\left( \\frac{2 \\, y \\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -2 \\, \\sqrt{y^{2} + 1} \\cos\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{2 \\, \\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{0} = \\left( \\frac{2 \\, y \\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( -2 \\, \\sqrt{y^{2} + 1} \\cos\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{2 \\, \\sin\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "K_0 = 2*y*sin(ta)/sqrt(y^2 + 1) ∂/∂ta - 2*sqrt(y^2 + 1)*cos(ta) ∂/∂y + 2*sin(ta)/sqrt(y^2 + 1) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{1} = \\left( \\frac{y \\cos\\left({\\tau}\\right) - \\sqrt{y^{2} + 1}}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( \\sqrt{y^{2} + 1} \\sin\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{1} = \\left( \\frac{y \\cos\\left({\\tau}\\right) - \\sqrt{y^{2} + 1}}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( \\sqrt{y^{2} + 1} \\sin\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "K_1 = (y*cos(ta) - sqrt(y^2 + 1))/sqrt(y^2 + 1) ∂/∂ta + sqrt(y^2 + 1)*sin(ta) ∂/∂y + cos(ta)/sqrt(y^2 + 1) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} = \\left( \\frac{y \\cos\\left({\\tau}\\right) + \\sqrt{y^{2} + 1}}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( \\sqrt{y^{2} + 1} \\sin\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} = \\left( \\frac{y \\cos\\left({\\tau}\\right) + \\sqrt{y^{2} + 1}}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\tau} } + \\left( \\sqrt{y^{2} + 1} \\sin\\left({\\tau}\\right) \\right) \\frac{\\partial}{\\partial y } + \\left( \\frac{\\cos\\left({\\tau}\\right)}{\\sqrt{y^{2} + 1}} \\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "K_2 = (y*cos(ta) + sqrt(y^2 + 1))/sqrt(y^2 + 1) ∂/∂ta + sqrt(y^2 + 1)*sin(ta) ∂/∂y + cos(ta)/sqrt(y^2 + 1) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{3} = \\frac{\\partial}{\\partial {\\theta} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{3} = \\frac{\\partial}{\\partial {\\theta} }$$" ], "text/plain": [ "K_3 = ∂/∂th" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for v in K:\n", " show(v.display())" ] }, { "cell_type": "markdown", "id": "c6cf1f72", "metadata": {}, "source": [ "We have then" ] }, { "cell_type": "code", "execution_count": 36, "id": "5c218299", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[K_{0},K_{1}\\right] = 2 K_{1}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[K_{0},K_{1}\\right] = 2 K_{1}$$" ], "text/plain": [ "[K_0,K_1] = 2 K_1" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K0.bracket(K1).display(K)" ] }, { "cell_type": "code", "execution_count": 37, "id": "590701df", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[K_{0},K_{2}\\right] = -2 K_{2}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[K_{0},K_{2}\\right] = -2 K_{2}$$" ], "text/plain": [ "[K_0,K_2] = -2 K_2" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K0.bracket(K2).display(K)" ] }, { "cell_type": "code", "execution_count": 38, "id": "f5156c82", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[K_{1},K_{2}\\right] = K_{0}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[K_{1},K_{2}\\right] = K_{0}$$" ], "text/plain": [ "[K_1,K_2] = K_0" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K1.bracket(K2).display(K)" ] }, { "cell_type": "markdown", "id": "623abeb9", "metadata": {}, "source": [ "The above commutation relations are exactly those of $\\mathfrak{sl}(2,\\mathbb{R})$ in the standard matrix representation:" ] }, { "cell_type": "code", "execution_count": 39, "id": "2a7c7909", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\left(\\begin{array}{rr}\n", "0 & 1 \\\\\n", "0 & 0\n", "\\end{array}\\right), \\left(\\begin{array}{rr}\n", "0 & 0 \\\\\n", "1 & 0\n", "\\end{array}\\right), \\left(\\begin{array}{rr}\n", "1 & 0 \\\\\n", "0 & -1\n", "\\end{array}\\right)\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\left(\\begin{array}{rr}\n", "0 & 1 \\\\\n", "0 & 0\n", "\\end{array}\\right), \\left(\\begin{array}{rr}\n", "0 & 0 \\\\\n", "1 & 0\n", "\\end{array}\\right), \\left(\\begin{array}{rr}\n", "1 & 0 \\\\\n", "0 & -1\n", "\\end{array}\\right)\\right)$$" ], "text/plain": [ "(\n", "[0 1] [0 0] [ 1 0]\n", "[0 0], [1 0], [ 0 -1]\n", ")" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sl2 = lie_algebras.sl(QQ, 2, representation='matrix') # QQ instead of RR to deal with an exact field\n", "E,F,H = sl2.gens()\n", "E,F,H" ] }, { "cell_type": "code", "execution_count": 40, "id": "ad8157c2", "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": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "all([H.bracket(E) == 2*E,\n", " H.bracket(F) == -2*F,\n", " E.bracket(F) == H])" ] }, { "cell_type": "markdown", "id": "88cfddb5", "metadata": {}, "source": [ "## Komar angular momentum \n", "\n", "The spacetime total **angular momentum** $J$ is computed from the axisymmetric Killing vector $\\eta$ via the Komar integral:\n", "$$J = \\frac{1}{16\\pi} \\oint_{\\mathscr{S}} \\star (\\mathrm{d}\\underline{\\eta})$$\n", "where \n", " - $\\mathrm{d}\\underline{\\eta}$ is the exterior derivative of the 1-form $\\underline{\\eta}$ (the $h$-dual to $\\eta$)\n", " - $\\star (\\mathrm{d}\\underline{\\eta})$ is the Hodge dual of $\\mathrm{d}\\underline{\\eta}$ with respect to $h$\n", " - $\\mathscr{S}$ is a closed spacelike 2-surface\n", " \n", "In vacuum, the Komar integral $J$ is independent of the choice of $\\mathscr{S}$. Let us choose $\\mathscr{S}$\n", "to be a sphere $(\\tau, y) = \\mathrm{const}$. We have then\n", "$$J = \\frac{1}{16\\pi} \\int_0^{2\\pi} \\int_0^\\pi \\left(\\star (\\mathrm{d}\\underline{\\eta}) \\right)_{\\theta\\psi} \\mathrm{d}\\theta\\; \\mathrm{d}\\psi$$ \n" ] }, { "cell_type": "markdown", "id": "86fa1ee5", "metadata": {}, "source": [ "The Killing vector $\\eta$:" ] }, { "cell_type": "code", "execution_count": 41, "id": "78cc9a19", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\eta = \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\eta = \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "eta = ∂/∂ps" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eta.display()" ] }, { "cell_type": "markdown", "id": "279a5a1f", "metadata": {}, "source": [ "The 1-form $\\underline{\\eta}$:" ] }, { "cell_type": "code", "execution_count": 42, "id": "0b7e8436", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\underline{\\eta} = \\left( \\frac{4 \\, y \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\psi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\underline{\\eta} = \\left( \\frac{4 \\, y \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\psi}$$" ], "text/plain": [ "ueta = 4*y*sin(th)^2/(cos(th)^2 + 1) dta + 4*sin(th)^2/(cos(th)^2 + 1) dps" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ueta = eta.down(h)\n", "ueta.set_name('ueta', latex_name=r'\\underline{\\eta}')\n", "ueta.display()" ] }, { "cell_type": "markdown", "id": "b8e8c4cd", "metadata": {}, "source": [ "The 2-form $\\mathrm{d}\\underline{\\eta}$:" ] }, { "cell_type": "code", "execution_count": 43, "id": "28f52fa0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\underline{\\eta} = \\left( -\\frac{4 \\, \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\wedge \\mathrm{d} y + \\left( -\\frac{16 \\, y \\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\wedge \\mathrm{d} {\\theta} + \\left( \\frac{16 \\, \\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\theta}\\wedge \\mathrm{d} {\\psi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\underline{\\eta} = \\left( -\\frac{4 \\, \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\wedge \\mathrm{d} y + \\left( -\\frac{16 \\, y \\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\wedge \\mathrm{d} {\\theta} + \\left( \\frac{16 \\, \\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\theta}\\wedge \\mathrm{d} {\\psi}$$" ], "text/plain": [ "dueta = -4*sin(th)^2/(cos(th)^2 + 1) dta∧dy - 16*y*cos(th)*sin(th)/(cos(th)^4 + 2*cos(th)^2 + 1) dta∧dth + 16*cos(th)*sin(th)/(cos(th)^4 + 2*cos(th)^2 + 1) dth∧dps" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "deta = diff(ueta)\n", "deta.display()" ] }, { "cell_type": "markdown", "id": "6f45ba60", "metadata": {}, "source": [ "The 2-form $\\star (\\mathrm{d}\\underline{\\eta})$:" ] }, { "cell_type": "code", "execution_count": 44, "id": "f8dde8e9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\star \\mathrm{d}\\underline{\\eta} = \\left( -\\frac{8 \\, \\sqrt{\\cos\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\theta}\\right) + 1} \\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)^{4} - 1} \\right) \\mathrm{d} {\\tau}\\wedge \\mathrm{d} y + \\left( -\\frac{8 \\, y \\sqrt{\\cos\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\theta}\\right) + 1} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\wedge \\mathrm{d} {\\theta} + \\left( \\frac{8 \\, \\sqrt{\\cos\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\theta}\\right) + 1} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\theta}\\wedge \\mathrm{d} {\\psi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\star \\mathrm{d}\\underline{\\eta} = \\left( -\\frac{8 \\, \\sqrt{\\cos\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\theta}\\right) + 1} \\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)^{4} - 1} \\right) \\mathrm{d} {\\tau}\\wedge \\mathrm{d} y + \\left( -\\frac{8 \\, y \\sqrt{\\cos\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\theta}\\right) + 1} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\tau}\\wedge \\mathrm{d} {\\theta} + \\left( \\frac{8 \\, \\sqrt{\\cos\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\theta}\\right) + 1} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\theta}\\wedge \\mathrm{d} {\\psi}$$" ], "text/plain": [ "*dueta = -8*sqrt(cos(th) + 1)*sqrt(-cos(th) + 1)*cos(th)*sin(th)/(cos(th)^4 - 1) dta∧dy - 8*y*sqrt(cos(th) + 1)*sqrt(-cos(th) + 1)*sin(th)^2/(cos(th)^4 + 2*cos(th)^2 + 1) dta∧dth + 8*sqrt(cos(th) + 1)*sqrt(-cos(th) + 1)*sin(th)^2/(cos(th)^4 + 2*cos(th)^2 + 1) dth∧dps" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sdeta = deta.hodge_dual()\n", "sdeta.display()" ] }, { "cell_type": "markdown", "id": "26f88ea2", "metadata": {}, "source": [ "The $\\theta\\psi$ component:" ] }, { "cell_type": "code", "execution_count": 45, "id": "0afab42c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{8 \\, \\sqrt{\\cos\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\theta}\\right) + 1} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{8 \\, \\sqrt{\\cos\\left({\\theta}\\right) + 1} \\sqrt{-\\cos\\left({\\theta}\\right) + 1} \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{4} + 2 \\, \\cos\\left({\\theta}\\right)^{2} + 1}$$" ], "text/plain": [ "8*sqrt(cos(th) + 1)*sqrt(-cos(th) + 1)*sin(th)^2/(cos(th)^4 + 2*cos(th)^2 + 1)" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sdeta23 = sdeta[2,3].expr()\n", "sdeta23" ] }, { "cell_type": "markdown", "id": "b2cfb970", "metadata": {}, "source": [ "This can be simplified to $\\frac{8\\sin^3\\theta}{(1 + \\cos^2\\theta)^2}$:" ] }, { "cell_type": "code", "execution_count": 46, "id": "a80ba495", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{8 \\, \\sin\\left({\\theta}\\right)^{3}}{{\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{8 \\, \\sin\\left({\\theta}\\right)^{3}}{{\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)}^{2}}$$" ], "text/plain": [ "8*sin(th)^3/(cos(th)^2 + 1)^2" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = 8*sin(th)^3/(1 + cos(th)^2)^2\n", "A" ] }, { "cell_type": "code", "execution_count": 47, "id": "cc624b25", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(sdeta23^2 - A^2).simplify_full()" ] }, { "cell_type": "markdown", "id": "fbacbaf7", "metadata": {}, "source": [ "Hence we have" ] }, { "cell_type": "code", "execution_count": 48, "id": "24c6b0d8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}1\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$$" ], "text/plain": [ "1" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "J_Komar = 1/(16*pi)*integrate(integrate(A, (th, 0, pi)), (ps, 0, 2*pi))\n", "J_Komar" ] }, { "cell_type": "markdown", "id": "ef09378f", "metadata": {}, "source": [ "If we restore the metric scale factor $m^2$, we have $h \\to m^2 h$, $\\underline{\\eta} \\to m^2 \\underline{\\eta}$, $\\mathrm{d}\\underline{\\eta} \\to m^2 \\mathrm{d}\\underline{\\eta}$ and $\\star(\\mathrm{d}\\underline{\\eta}) \\to m^2 \\star(\\mathrm{d}\\underline{\\eta})$. The last property holds because in dimension 4, the Hodge dual is conformally invariant on 2-forms (as it can be easily checked from its definition). \n", "Hence we conclude that\n", "$$J = m^2$$\n", "In other words, **the angular momentum of the NHEK spacetime is identical to the angular momentum of the Kerr spacetime from which it derives.** " ] }, { "cell_type": "markdown", "id": "cfd3464e", "metadata": {}, "source": [ "For the record:" ] }, { "cell_type": "code", "execution_count": 49, "id": "3f53b756", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}8\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}8$$" ], "text/plain": [ "8" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate(A, (th, 0, pi))" ] }, { "cell_type": "code", "execution_count": 50, "id": "c80bef77", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{8 \\, \\cos\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)^{2} + 1}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{8 \\, \\cos\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)^{2} + 1}$$" ], "text/plain": [ "-8*cos(th)/(cos(th)^2 + 1)" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate(A, th)" ] }, { "cell_type": "code", "execution_count": 51, "id": "8c850924", "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": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bool(diff(_, th) == A) # a check" ] }, { "cell_type": "markdown", "id": "54028180", "metadata": {}, "source": [ "## Conformal global coordinates\n", "\n", "Let us introduce the \"conformal\" global coordinates $(\\tau,\\chi,\\theta,\\psi)$ such that $y = \\tan\\chi$:" ] }, { "cell_type": "code", "execution_count": 52, "id": "4c7ef689", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (N, (ta, ch, th, ps))\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N},({\\tau}, {\\chi}, {\\theta}, {\\psi})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N},({\\tau}, {\\chi}, {\\theta}, {\\psi})\\right)$$" ], "text/plain": [ "Chart (N, (ta, ch, th, ps))" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC. = N.chart(r\"ta:\\tau ch:(-pi/2,pi/2):\\chi th:(0,pi):\\theta ps:(0,2*pi):periodic:\\psi\") \n", "print(XC)\n", "XC" ] }, { "cell_type": "code", "execution_count": 53, "id": "d1d3a3b2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\chi} :\\ \\left( -\\frac{1}{2} \\, \\pi , \\frac{1}{2} \\, \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\psi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\chi} :\\ \\left( -\\frac{1}{2} \\, \\pi , \\frac{1}{2} \\, \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\psi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}$$" ], "text/plain": [ "ta: (-oo, +oo); ch: (-1/2*pi, 1/2*pi); th: (0, pi); ps: [0, 2*pi] (periodic)" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC.coord_range()" ] }, { "cell_type": "code", "execution_count": 54, "id": "408198fc", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & {\\tau} \\\\ {\\chi} & = & \\arctan\\left(y\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\psi} & = & {\\psi} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & {\\tau} \\\\ {\\chi} & = & \\arctan\\left(y\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\psi} & = & {\\psi} \\end{array}\\right.$$" ], "text/plain": [ "ta = ta\n", "ch = arctan(y)\n", "th = th\n", "ps = ps" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_to_XC = X.transition_map(XC, [ta, atan(y), th, ps])\n", "X_to_XC.display()" ] }, { "cell_type": "code", "execution_count": 55, "id": "7c23bf28", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & {\\tau} \\\\ y & = & \\frac{\\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\psi} & = & {\\psi} \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & {\\tau} \\\\ y & = & \\frac{\\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\psi} & = & {\\psi} \\end{array}\\right.$$" ], "text/plain": [ "ta = ta\n", "y = sin(ch)/cos(ch)\n", "th = th\n", "ps = ps" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_to_XC.inverse().display()" ] }, { "cell_type": "code", "execution_count": 56, "id": "b647c26c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = \\left( -\\frac{\\sin\\left({\\theta}\\right)^{4} + 4 \\, {\\left(\\cos\\left({\\chi}\\right)^{2} - 2\\right)} \\sin\\left({\\theta}\\right)^{2} + 4}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\psi} + \\left( \\frac{\\cos\\left({\\theta}\\right)^{2} + 1}{\\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\left( \\cos\\left({\\theta}\\right)^{2} + 1 \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{4 \\, \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\psi}\\otimes \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\psi}\\otimes \\mathrm{d} {\\psi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = \\left( -\\frac{\\sin\\left({\\theta}\\right)^{4} + 4 \\, {\\left(\\cos\\left({\\chi}\\right)^{2} - 2\\right)} \\sin\\left({\\theta}\\right)^{2} + 4}{\\cos\\left({\\chi}\\right)^{2} \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\psi} + \\left( \\frac{\\cos\\left({\\theta}\\right)^{2} + 1}{\\cos\\left({\\chi}\\right)^{2}} \\right) \\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\left( \\cos\\left({\\theta}\\right)^{2} + 1 \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{4 \\, \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\chi}\\right) \\cos\\left({\\theta}\\right)^{2} + \\cos\\left({\\chi}\\right)} \\right) \\mathrm{d} {\\psi}\\otimes \\mathrm{d} {\\tau} + \\left( \\frac{4 \\, \\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2} + 1} \\right) \\mathrm{d} {\\psi}\\otimes \\mathrm{d} {\\psi}$$" ], "text/plain": [ "h = -(sin(th)^4 + 4*(cos(ch)^2 - 2)*sin(th)^2 + 4)/(cos(ch)^2*cos(th)^2 + cos(ch)^2) dta⊗dta + 4*sin(ch)*sin(th)^2/(cos(ch)*cos(th)^2 + cos(ch)) dta⊗dps + (cos(th)^2 + 1)/cos(ch)^2 dch⊗dch + (cos(th)^2 + 1) dth⊗dth + 4*sin(ch)*sin(th)^2/(cos(ch)*cos(th)^2 + cos(ch)) dps⊗dta + 4*sin(th)^2/(cos(th)^2 + 1) dps⊗dps" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.display(XC)" ] }, { "cell_type": "markdown", "id": "7fd95632", "metadata": {}, "source": [ "### Expression of the Killing vectors in terms of conformal coordinates:" ] }, { "cell_type": "code", "execution_count": 57, "id": "7a2322fa", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{0} = \\frac{\\partial}{\\partial {\\tau} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{0} = \\frac{\\partial}{\\partial {\\tau} }$$" ], "text/plain": [ "J_0 = ∂/∂ta" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{1} = \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\tau} } -\\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{1} = \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\tau} } -\\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "J_1 = sin(ch)*sin(ta) ∂/∂ta - cos(ch)*cos(ta) ∂/∂ch + cos(ch)*sin(ta) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{2} = \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\frac{\\partial}{\\partial {\\tau} } + \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{2} = \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) \\frac{\\partial}{\\partial {\\tau} } + \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "J_2 = cos(ta)*sin(ch) ∂/∂ta + cos(ch)*sin(ta) ∂/∂ch + cos(ch)*cos(ta) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for v in J[:-1]:\n", " show(v.display(XC))" ] }, { "cell_type": "code", "execution_count": 58, "id": "f527cfdd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{0} = 2 \\, \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\tau} } -2 \\, \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + 2 \\, \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{0} = 2 \\, \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\tau} } -2 \\, \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + 2 \\, \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "K_0 = 2*sin(ch)*sin(ta) ∂/∂ta - 2*cos(ch)*cos(ta) ∂/∂ch + 2*cos(ch)*sin(ta) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{1} = \\left( \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) - 1 \\right) \\frac{\\partial}{\\partial {\\tau} } + \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{1} = \\left( \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) - 1 \\right) \\frac{\\partial}{\\partial {\\tau} } + \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "K_1 = (cos(ta)*sin(ch) - 1) ∂/∂ta + cos(ch)*sin(ta) ∂/∂ch + cos(ch)*cos(ta) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} = \\left( \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) + 1 \\right) \\frac{\\partial}{\\partial {\\tau} } + \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} = \\left( \\cos\\left({\\tau}\\right) \\sin\\left({\\chi}\\right) + 1 \\right) \\frac{\\partial}{\\partial {\\tau} } + \\cos\\left({\\chi}\\right) \\sin\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\chi} } + \\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) \\frac{\\partial}{\\partial {\\psi} }$$" ], "text/plain": [ "K_2 = (cos(ta)*sin(ch) + 1) ∂/∂ta + cos(ch)*sin(ta) ∂/∂ch + cos(ch)*cos(ta) ∂/∂ps" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for v in K[:-1]:\n", " show(v.display(XC))" ] }, { "cell_type": "markdown", "id": "4a11c673", "metadata": {}, "source": [ "## Poincaré patch" ] }, { "cell_type": "code", "execution_count": 59, "id": "4e61f840", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset NP of the 4-dimensional Lorentzian manifold N\n" ] } ], "source": [ "NP = N.open_subset('NP', latex_name=r'\\mathscr{N}_{\\rm P}',\n", " coord_def={XC: [-ch - pi/2 < ta, ta < - ch - 3*pi/2]})\n", "print(NP)" ] }, { "cell_type": "code", "execution_count": 60, "id": "4fb28010", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Chart (NP, (T, R, th, Ph))\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N}_{\\rm P},(T, R, {\\theta}, {\\Phi})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathscr{N}_{\\rm P},(T, R, {\\theta}, {\\Phi})\\right)$$" ], "text/plain": [ "Chart (NP, (T, R, th, Ph))" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XP. = NP.chart(r\"T R th:(0,pi):\\theta Ph:(0,2*pi):periodic:\\Phi\")\n", "print(XP)\n", "XP" ] }, { "cell_type": "code", "execution_count": 61, "id": "989e4a6a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} T & = & \\frac{\\sin\\left({\\tau}\\right)}{\\cos\\left({\\tau}\\right) + \\sin\\left({\\chi}\\right)} \\\\ R & = & \\frac{\\cos\\left({\\tau}\\right) + \\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\Phi} & = & {\\psi} + \\log\\left(\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) + \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right) + \\sin\\left({\\tau}\\right)}\\right) \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} T & = & \\frac{\\sin\\left({\\tau}\\right)}{\\cos\\left({\\tau}\\right) + \\sin\\left({\\chi}\\right)} \\\\ R & = & \\frac{\\cos\\left({\\tau}\\right) + \\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\Phi} & = & {\\psi} + \\log\\left(\\frac{\\cos\\left({\\chi}\\right) \\cos\\left({\\tau}\\right) + \\sin\\left({\\chi}\\right) \\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right) + \\sin\\left({\\tau}\\right)}\\right) \\end{array}\\right.$$" ], "text/plain": [ "T = sin(ta)/(cos(ta) + sin(ch))\n", "R = (cos(ta) + sin(ch))/cos(ch)\n", "th = th\n", "Ph = ps + log((cos(ch)*cos(ta) + sin(ch)*sin(ta))/(cos(ch) + sin(ta)))" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Conf_to_Poinc = XC.transition_map(XP, [sin(ta)/(cos(ta) + sin(ch)),\n", " (cos(ta) + sin(ch))/cos(ch),\n", " th,\n", " ps + log((cos(ta)*cos(ch) + sin(ta)*sin(ch))/(sin(ta) + cos(ch)))])\n", "Conf_to_Poinc.display()" ] }, { "cell_type": "code", "execution_count": 62, "id": "7b5fcebf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " ta == pi*unit_step(-(cos(ta) + sin(ch))/cos(ch)) + arctan2(2*(cos(ta) + sin(ch))*sin(ta)/cos(ch)^2, 2*(cos(ta)^2 + cos(ta)*sin(ch))/cos(ch)^2) **failed**\n", " ch == arctan(sin(ch)/cos(ch)) **failed**\n", " th == th *passed*\n", " ps == ps *passed*\n", " T == (R^3*T^2*sin(pi*unit_step(-R)) - 2*R^3*T*cos(pi*unit_step(-R)) - R^3*sin(pi*unit_step(-R)) - R*sin(pi*unit_step(-R)))/(2*R^3*T*sin(pi*unit_step(-R)) - R^3*cos(pi*unit_step(-R)) + (R^3*cos(pi*unit_step(-R)) - R^2*abs(R))*T^2 - (R^2 - 1)*abs(R) - R*cos(pi*unit_step(-R))) **failed**\n", " R == -1/2*(2*R^3*T*sin(pi*unit_step(-R)) - R^3*cos(pi*unit_step(-R)) + (R^3*cos(pi*unit_step(-R)) - R^2*abs(R))*T^2 - (R^2 - 1)*abs(R) - R*cos(pi*unit_step(-R)))/(R*abs(R)) **failed**\n", " th == th *passed*\n", " Ph == Ph + log((R^2*T^2*abs(R)*sin(pi*unit_step(-R)) - 2*(R^2*cos(pi*unit_step(-R)) - R*sin(pi*unit_step(-R)))*T*abs(R) - (R^2*sin(pi*unit_step(-R)) + 2*R*cos(pi*unit_step(-R)) - sin(pi*unit_step(-R)))*abs(R))/(R^3*T^2*sin(pi*unit_step(-R)) - 2*R^3*T*cos(pi*unit_step(-R)) - R^3*sin(pi*unit_step(-R)) - 2*R*abs(R) - R*sin(pi*unit_step(-R)))) **failed**\n", "NB: a failed report can reflect a mere lack of simplification.\n" ] } ], "source": [ "Conf_to_Poinc.set_inverse(atan2(2*R^2*T, R^2*(1 - T^2) +1) + pi*unit_step(-R),\n", " atan((R^2*(1 + T^2) - 1)/(2*R)),\n", " th,\n", " Ph - ln(((1 - T*R)^2 + R^2)/sqrt(((1 + T^2)*R^2 - 1)^2 + 4*R^2)))" ] }, { "cell_type": "code", "execution_count": 63, "id": "b44ea5c0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & \\pi \\mathrm{u}\\left(-R\\right) + \\arctan\\left(2 \\, R^{2} T, -{\\left(T^{2} - 1\\right)} R^{2} + 1\\right) \\\\ {\\chi} & = & \\arctan\\left(\\frac{{\\left(T^{2} + 1\\right)} R^{2} - 1}{2 \\, R}\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\psi} & = & {\\Phi} - \\log\\left(\\frac{{\\left(R T - 1\\right)}^{2} + R^{2}}{\\sqrt{{\\left({\\left(T^{2} + 1\\right)} R^{2} - 1\\right)}^{2} + 4 \\, R^{2}}}\\right) \\end{array}\\right.\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & \\pi \\mathrm{u}\\left(-R\\right) + \\arctan\\left(2 \\, R^{2} T, -{\\left(T^{2} - 1\\right)} R^{2} + 1\\right) \\\\ {\\chi} & = & \\arctan\\left(\\frac{{\\left(T^{2} + 1\\right)} R^{2} - 1}{2 \\, R}\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\psi} & = & {\\Phi} - \\log\\left(\\frac{{\\left(R T - 1\\right)}^{2} + R^{2}}{\\sqrt{{\\left({\\left(T^{2} + 1\\right)} R^{2} - 1\\right)}^{2} + 4 \\, R^{2}}}\\right) \\end{array}\\right.$$" ], "text/plain": [ "ta = pi*unit_step(-R) + arctan2(2*R^2*T, -(T^2 - 1)*R^2 + 1)\n", "ch = arctan(1/2*((T^2 + 1)*R^2 - 1)/R)\n", "th = th\n", "ps = Ph - log(((R*T - 1)^2 + R^2)/sqrt(((T^2 + 1)*R^2 - 1)^2 + 4*R^2))" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Conf_to_Poinc.inverse().display()" ] }, { "cell_type": "code", "execution_count": 64, "id": "ebbc91d3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 34 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_XP = XP.plot(chart=XC, ambient_coords=(ch, ta), fixed_coords={th: pi/2, Ph: 0},\n", " ranges={T: (-9, 9), R: (-9, 8)}, color={T: 'red', R: 'grey'},\n", " number_values=17, plot_points=200)\n", "show(graph_XP, aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 65, "id": "fdc67f4b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathscr{N}_{\\rm P}^+\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathscr{N}_{\\rm P}^+$$" ], "text/plain": [ "Open subset NP1 of the 4-dimensional Lorentzian manifold N" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "NP1 = NP.open_subset('NP1', latex_name=r'\\mathscr{N}_{\\rm P}^+',\n", " coord_def={XP: R>0})\n", "NP1" ] }, { "cell_type": "code", "execution_count": 66, "id": "d18099f2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{0} = \\left( \\frac{R^{2} T^{2} + R^{2} + 1}{2 \\, R^{2}} \\right) \\frac{\\partial}{\\partial T } -R T \\frac{\\partial}{\\partial R } -\\frac{1}{R} \\frac{\\partial}{\\partial {\\Phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{0} = \\left( \\frac{R^{2} T^{2} + R^{2} + 1}{2 \\, R^{2}} \\right) \\frac{\\partial}{\\partial T } -R T \\frac{\\partial}{\\partial R } -\\frac{1}{R} \\frac{\\partial}{\\partial {\\Phi} }$$" ], "text/plain": [ "J_0 = 1/2*(R^2*T^2 + R^2 + 1)/R^2 ∂/∂T - R*T ∂/∂R - 1/R ∂/∂Ph" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{1} = T \\frac{\\partial}{\\partial T } -R \\frac{\\partial}{\\partial R }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{1} = T \\frac{\\partial}{\\partial T } -R \\frac{\\partial}{\\partial R }$$" ], "text/plain": [ "J_1 = T ∂/∂T - R ∂/∂R" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{2} = \\left( -\\frac{R^{2} T^{2} - R^{2} + 1}{2 \\, R^{2}} \\right) \\frac{\\partial}{\\partial T } + R T \\frac{\\partial}{\\partial R } + \\frac{1}{R} \\frac{\\partial}{\\partial {\\Phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{2} = \\left( -\\frac{R^{2} T^{2} - R^{2} + 1}{2 \\, R^{2}} \\right) \\frac{\\partial}{\\partial T } + R T \\frac{\\partial}{\\partial R } + \\frac{1}{R} \\frac{\\partial}{\\partial {\\Phi} }$$" ], "text/plain": [ "J_2 = -1/2*(R^2*T^2 - R^2 + 1)/R^2 ∂/∂T + R*T ∂/∂R + 1/R ∂/∂Ph" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with assuming(R>0):\n", " for v in J[:-1]:\n", " show(v.display(XP))" ] }, { "cell_type": "code", "execution_count": 67, "id": "2f5ac116", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{0} = 2 \\, T \\frac{\\partial}{\\partial T } -2 \\, R \\frac{\\partial}{\\partial R }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{0} = 2 \\, T \\frac{\\partial}{\\partial T } -2 \\, R \\frac{\\partial}{\\partial R }$$" ], "text/plain": [ "K_0 = 2*T ∂/∂T - 2*R ∂/∂R" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{1} = \\left( -\\frac{R^{2} T^{2} + 1}{R^{2}} \\right) \\frac{\\partial}{\\partial T } + 2 \\, R T \\frac{\\partial}{\\partial R } + \\frac{2}{R} \\frac{\\partial}{\\partial {\\Phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{1} = \\left( -\\frac{R^{2} T^{2} + 1}{R^{2}} \\right) \\frac{\\partial}{\\partial T } + 2 \\, R T \\frac{\\partial}{\\partial R } + \\frac{2}{R} \\frac{\\partial}{\\partial {\\Phi} }$$" ], "text/plain": [ "K_1 = -(R^2*T^2 + 1)/R^2 ∂/∂T + 2*R*T ∂/∂R + 2/R ∂/∂Ph" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} = \\frac{\\partial}{\\partial T }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}K_{2} = \\frac{\\partial}{\\partial T }$$" ], "text/plain": [ "K_2 = ∂/∂T" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with assuming(R>0):\n", " for v in K[:-1]:\n", " show(v.display(XP))" ] }, { "cell_type": "markdown", "id": "8d910967", "metadata": {}, "source": [ "### Plot of the Killing vector $J_1$" ] }, { "cell_type": "code", "execution_count": 68, "id": "465d05e1", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 146 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_J1 = J1.plot(chart=XC, ambient_coords=(ch, ta), chart_domain=XC, \n", " fixed_coords={th: pi/2, ps: 0}, ranges={ta: (-pi, 2*pi)}, \n", " number_values={ta: 16, ch: 7},\n", " color='purple', scale=0.4, arrowsize=2)\n", "graph = graph_XP + graph_J1\n", "show(graph, figsize=8)" ] }, { "cell_type": "markdown", "id": "82f4acef", "metadata": {}, "source": [ "### Plot of the Killing vector $K_1$" ] }, { "cell_type": "code", "execution_count": 69, "id": "4e11d785", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 146 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_K1 = K1.plot(chart=XC, ambient_coords=(ch, ta), chart_domain=XC, \n", " fixed_coords={th: pi/2, ps: 0}, ranges={ta: (-pi, 2*pi)}, \n", " number_values={ta: 16, ch: 7},\n", " color='blue', scale=0.4, arrowsize=2)\n", "graph = graph_XP + graph_K1\n", "show(graph, figsize=8)" ] }, { "cell_type": "markdown", "id": "ac6a967c", "metadata": {}, "source": [ "## Plot of Poincaré patches with $T=\\mathrm{const}$ and $R=\\mathrm{const}$ hypersurfaces" ] }, { "cell_type": "code", "execution_count": 70, "id": "0245403f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( T, R \\right) \\ {\\mapsto} \\ \\pi \\mathrm{u}\\left(-R\\right) + \\arctan\\left(2 \\, R^{2} T, -R^{2} T^{2} + R^{2} + 1\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( T, R \\right) \\ {\\mapsto} \\ \\pi \\mathrm{u}\\left(-R\\right) + \\arctan\\left(2 \\, R^{2} T, -R^{2} T^{2} + R^{2} + 1\\right)$$" ], "text/plain": [ "(T, R) |--> pi*unit_step(-R) + arctan2(2*R^2*T, -R^2*T^2 + R^2 + 1)" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "taf = (Conf_to_Poinc.inverse()(T, R, 0, 0)[0]).function(T, R)\n", "taf" ] }, { "cell_type": "code", "execution_count": 71, "id": "45fb7d96", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( T, R \\right) \\ {\\mapsto} \\ \\arctan\\left(\\frac{R^{2} T^{2} + R^{2} - 1}{2 \\, R}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( T, R \\right) \\ {\\mapsto} \\ \\arctan\\left(\\frac{R^{2} T^{2} + R^{2} - 1}{2 \\, R}\\right)$$" ], "text/plain": [ "(T, R) |--> arctan(1/2*(R^2*T^2 + R^2 - 1)/R)" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chf = (Conf_to_Poinc.inverse()(T, R, 0, 0)[1]).function(T, R)\n", "chf" ] }, { "cell_type": "code", "execution_count": 72, "id": "1eee1925", "metadata": {}, "outputs": [], "source": [ "def plot_p(n, T_values=None, R_min=0.0001, R_max=100, \n", " color_T='dimgray', linestyle_T='-', \n", " R_values=None, T_min=-100, T_max=100, \n", " color_R='red', linestyle_R='-'):\n", " n2 = 2*n\n", " res = polygon([(pi/2, (n2 - 1)*pi), (-pi/2, n2*pi), (pi/2, (n2 + 1)*pi)], \n", " color='white', edgecolor='black')\n", " res += line([(pi/2, (n2 - 1)*pi), (-pi/2, n2*pi), (pi/2, (n2 + 1)*pi)], \n", " color='black', thickness=3)\n", " if T_values is not None:\n", " for T0 in T_values:\n", " res += parametric_plot((chf(T0, R), taf(T0, R) + n2*pi), (R, R_min, R_max), \n", " color=color_T, linestyle=linestyle_T)\n", " if R_values is not None:\n", " for R0 in R_values:\n", " res += parametric_plot((chf(T, R0), taf(T, R0) + n2*pi), (T, T_min, T_max), \n", " color=color_R, linestyle=linestyle_R)\n", " return res\n", "\n", "\n", "def plot_m(n, T_values=None, R_min=-100, R_max=-0.0001, \n", " color_T='dimgray', linestyle_T='-', \n", " R_values=None, T_min=-100, T_max=100, \n", " color_R='red', linestyle_R='-'):\n", " n2 = 2*n\n", " res = polygon([(-pi/2, n2*pi), (pi/2, (n2 + 1)*pi), (-pi/2, (n2 + 2)*pi)], \n", " color='cornsilk', edgecolor='black')\n", " res += line([(-pi/2, n2*pi), (pi/2, (n2 + 1)*pi), (-pi/2, (n2 + 2)*pi)], \n", " color='black', thickness=3)\n", " if T_values is not None:\n", " for T0 in T_values:\n", " res += parametric_plot((chf(T0, R), taf(T0, R) + n2*pi), (R, R_min, R_max), \n", " color=color_T, linestyle=linestyle_T)\n", " if R_values is not None:\n", " for R0 in R_values:\n", " res += parametric_plot((chf(T, R0), taf(T, R0) + n2*pi), (T, T_min, T_max), \n", " color=color_R, linestyle=linestyle_R)\n", " return res\n", "\n" ] }, { "cell_type": "code", "execution_count": 73, "id": "2363c7fa", "metadata": {}, "outputs": [], "source": [ "R_val_p = [0.2, 0.4, 0.6, 0.8, 1]\n", "R_val_m = [-1, -0.8, -0.6, -0.4, -0.2] \n", "T_val = [-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]" ] }, { "cell_type": "code", "execution_count": 74, "id": "d680f64f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics Array of size 1 x 2" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graphics_array([plot_p(0, T_values=T_val, R_max=R_val_p[-1], R_values=R_val_p),\n", " plot_m(0, T_values=T_val, R_min=R_val_m[0], R_values=R_val_m)])" ] }, { "cell_type": "code", "execution_count": 75, "id": "481009bf", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 98 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = Graphics()\n", "for n in [-1, 0, 1]:\n", " graph += plot_p(n, T_values=T_val, R_max=R_val_p[-1], R_values=R_val_p)\n", " graph += plot_m(n, T_values=T_val, R_min=R_val_m[0], R_values=R_val_m)\n", "graph += line([(-pi/2, -4), (-pi/2, 8)], color='darkmagenta', thickness=2) \\\n", " + line([(pi/2, -4), (pi/2, 8)], color='darkmagenta', thickness=2)\n", "graph.axes_labels([r'$\\chi$', r'$\\tau$'])\n", "show(graph, ymin=-pi, ymax=2*pi, frame=True, axes=False, figsize=10)" ] }, { "cell_type": "markdown", "id": "bb553a87", "metadata": {}, "source": [ "Adding some labels:" ] }, { "cell_type": "code", "execution_count": 76, "id": "88ef46c9", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 105 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph += text(r\"$R=\\!+\\infty$\", (pi/2+0.25, 0), rotation=90, color='darkmagenta',\n", " fontsize=16) \\\n", " + text(r\"$R=\\!-\\infty$\", (-pi/2-0.2, pi), rotation=90, color='darkmagenta',\n", " fontsize=16) \\\n", " + text(r\"$R=1$\", (0.75, 1), rotation=55, color='red', fontsize=16) \\\n", " + text(r\"$R=\\!-1$\", (-0.8, 2), rotation=55, color='red', fontsize=16) \\\n", " + text(r\"$R=0$\", (-0.15, pi/2+0.15), rotation=45, color='black', fontsize=16) \\\n", " + text(r\"$\\mathscr{N}_{\\rm P}^+$\", (0.9, 0), color='black', fontsize=18) \\\n", " + text(r\"$\\mathscr{N}_{\\rm P}^-$\", (-0.9, pi), color='black', fontsize=18)\n", "graph.axes_labels([r'$\\chi$', r'$\\tau$'])\n", "graph.save(\"exk_NHEK_spacetime.pdf\", xmin=-2.2, xmax=2.2, ymin=-pi, ymax=2*pi, \n", " frame=True, axes=False, figsize=9)\n", "show(graph, xmin=-2.2, xmax=2.2, ymin=-pi, ymax=2*pi, frame=True, axes=False, figsize=9)" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5.beta2", "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": 5 }