{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Conformal completion of Minkowski spacetime\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](http://luth.obspm.fr/~luthier/gourgoulhon/bh16/)\n", " \n", "It makes use of SageMath differential geometry tools developed through the \n", "[SageManifolds](http://sagemanifolds.obspm.fr) project." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 7.5 is required to run this notebook: " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.3.rc4, Release Date: 2021-04-18'" ] }, "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 formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spherical coordinates on Minkowski spacetime\n", "\n", "We declare the spacetime manifold $M$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional differentiable manifold M\n" ] } ], "source": [ "M = Manifold(4, 'M')\n", "print(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and the spherical coordinates $(t,r,\\theta,\\phi)$ as a chart on $M$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,(t, r, {\\theta}, {\\phi})\\right)$$" ], "text/plain": [ "Chart (M, (t, r, th, ph))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS. = M.chart(r't r:(0,+oo) th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "XS" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( 0 , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$$" ], "text/plain": [ "t: (-oo, +oo); r: (0, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In term of these coordinates, the Minkowski metric is" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = -\\mathrm{d} t\\otimes \\mathrm{d} t+\\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "g = -dt*dt + dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = M.lorentzian_metric('g')\n", "g[0,0] = -1\n", "g[1,1] = 1\n", "g[2,2] = r^2\n", "g[3,3] = r^2*sin(th)^2\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Null coordinates\n", "\n", "Let us introduce the null coordinates $u=t-r$ (retarded time) and $v=t+r$ (advanced time):" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,(u, v, {\\theta}, {\\phi})\\right)$$" ], "text/plain": [ "Chart (M, (u, v, th, ph))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN. = M.chart(r'u v th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "XN.add_restrictions(v-u>0)\n", "XN" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}u :\\ \\left( -\\infty, +\\infty \\right) ;\\quad v :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$$" ], "text/plain": [ "u: (-oo, +oo); v: (-oo, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN.coord_range()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} u & = & -r + t \\\\ v & = & r + t \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "u = -r + t\n", "v = r + t\n", "th = th\n", "ph = ph" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XN = XS.transition_map(XN, [t-r, t+r, th, ph])\n", "XS_to_XN.display()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & \\frac{1}{2} \\, u + \\frac{1}{2} \\, v \\\\ r & = & -\\frac{1}{2} \\, u + \\frac{1}{2} \\, v \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "t = 1/2*u + 1/2*v\n", "r = -1/2*u + 1/2*v\n", "th = th\n", "ph = ph" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XN.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In terms of the null coordinates $(u,v,\\theta,\\phi)$, the Minkowski metric writes" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = -\\frac{1}{2} \\mathrm{d} u\\otimes \\mathrm{d} v -\\frac{1}{2} \\mathrm{d} v\\otimes \\mathrm{d} u + \\left( \\frac{1}{4} \\, u^{2} - \\frac{1}{2} \\, u v + \\frac{1}{4} \\, v^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{1}{4} \\, u^{2} \\sin\\left({\\theta}\\right)^{2} - \\frac{1}{2} \\, u v \\sin\\left({\\theta}\\right)^{2} + \\frac{1}{4} \\, v^{2} \\sin\\left({\\theta}\\right)^{2} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "g = -1/2 du*dv - 1/2 dv*du + (1/4*u^2 - 1/2*u*v + 1/4*v^2) dth*dth + (1/4*u^2*sin(th)^2 - 1/2*u*v*sin(th)^2 + 1/4*v^2*sin(th)^2) dph*dph" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(XN.frame(), XN)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us plot the coordinate grid $(u,v)$ in terms of the coordinates $(t,r)$:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 33 graphics primitives" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = XN.plot(XS, ambient_coords=(r,t), fixed_coords={th: pi/2, ph: pi}, \n", " number_values=17, plot_points=200, color='green', \n", " style={u: '--', v: '-'}, thickness=1.5)\n", "graph" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 33 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph, xmin=0, xmax=4, ymin=0, ymax=4, aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "graph.save(\"glo_null_coord.pdf\", xmin=0, xmax=4, ymin=0, ymax=4, \n", " aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compactified null coordinates\n", "\n", "Instead of $(u,v)$, which span $\\mathbb{R}$, let consider the coordinates $U = \\mathrm{atan}\\, u$ and $V = \\mathrm{atan}\\, v$, which span $\\left(-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right)$:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = plot(atan(u), (u,-6, 6), thickness=2, axes_labels=[r'$u$', r'$U$']) \\\n", " + line([(-6,-pi/2), (6,-pi/2)], linestyle='--') \\\n", " + line([(-6,pi/2), (6,pi/2)], linestyle='--')\n", "show(graph, aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "graph.save('glo_atan.pdf', aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,(U, V, {\\theta}, {\\phi})\\right)$$" ], "text/plain": [ "Chart (M, (U, V, th, ph))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XNC. = M.chart(r'U:(-pi/2,pi/2) V:(-pi/2,pi/2) th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "XNC.add_restrictions(V-U>0)\n", "XNC" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}U :\\ \\left( -\\frac{1}{2} \\, \\pi , \\frac{1}{2} \\, \\pi \\right) ;\\quad V :\\ \\left( -\\frac{1}{2} \\, \\pi , \\frac{1}{2} \\, \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$$" ], "text/plain": [ "U: (-1/2*pi, 1/2*pi); V: (-1/2*pi, 1/2*pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XNC.coord_range()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} U & = & \\arctan\\left(u\\right) \\\\ V & = & \\arctan\\left(v\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "U = arctan(u)\n", "V = arctan(v)\n", "th = th\n", "ph = ph" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN_to_XNC = XN.transition_map(XNC, [atan(u), atan(v), th, ph])\n", "XN_to_XNC.display()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} u & = & \\frac{\\sin\\left(U\\right)}{\\cos\\left(U\\right)} \\\\ v & = & \\frac{\\sin\\left(V\\right)}{\\cos\\left(V\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "u = sin(U)/cos(U)\n", "v = sin(V)/cos(V)\n", "th = th\n", "ph = ph" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN_to_XNC.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expressed in terms of the coordinates $(U,V,\\theta,\\phi)$, the metric tensor is" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} U\\otimes \\mathrm{d} V -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} V\\otimes \\mathrm{d} U + \\left( \\frac{\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\left(\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "g = -1/2/(cos(U)^2*cos(V)^2) dU*dV - 1/2/(cos(U)^2*cos(V)^2) dV*dU + 1/4*(cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2)/(cos(U)^2*cos(V)^2) dth*dth + 1/4*(cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2)*sin(th)^2/(cos(U)^2*cos(V)^2) dph*dph" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(XNC.frame(), XNC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us call $\\Omega^{-2}$ the common factor: " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{u^{2} + 1} \\sqrt{v^{2} + 1}} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\end{array}$$" ], "text/plain": [ "Omega: M --> R\n", " (u, v, th, ph) |--> 2/(sqrt(u^2 + 1)*sqrt(v^2 + 1))\n", " (U, V, th, ph) |--> 2*cos(U)*cos(V)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega = M.scalar_field({XNC: 2*cos(U)*cos(V)}, name='Omega', latex_name=r'\\Omega')\n", "Omega.display()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}} \\end{array}$$" ], "text/plain": [ "Omega: M --> R\n", " (t, r, th, ph) |--> 2/(sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1))" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.display(XS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conformal metric\n", "\n", "We introduce the metric $\\tilde g = \\Omega^2 g$:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{g} = -2 \\mathrm{d} U\\otimes \\mathrm{d} V -2 \\mathrm{d} V\\otimes \\mathrm{d} U + \\left( \\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + {\\left(\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "gt = -2 dU*dV - 2 dV*dU + (cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2) dth*dth + (cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2)*sin(th)^2 dph*dph" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt = M.lorentzian_metric('gt', latex_name=r'\\tilde{g}')\n", "gt.set(Omega^2*g)\n", "gt.display(XNC.frame(), XNC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly the metric components ${\\tilde g}_{\\theta\\theta}$ and ${\\tilde g}_{\\phi\\phi}$ can be simplified further. Let us do it by hand, by extracting the symbolic expression via `expr()`:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}$$" ], "text/plain": [ "cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g22 = gt[XNC.frame(), 2, 2, XNC].expr()\n", "g22" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left(-U + V\\right)^{2}$$" ], "text/plain": [ "sin(-U + V)^2" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g22.factor().reduce_trig()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}$$" ], "text/plain": [ "cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g33st = gt[XNC.frame(), 3, 3, XNC].expr() / sin(th)^2\n", "g33st" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left(-U + V\\right)^{2}$$" ], "text/plain": [ "sin(-U + V)^2" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g33st.factor().reduce_trig()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "gt.add_comp(XNC.frame())[2,2, XNC] = g22.factor().reduce_trig()\n", "gt.add_comp(XNC.frame())[3,3, XNC] = g33st.factor().reduce_trig() * sin(th)^2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence the final form of the conformal metric in terms of the compactified null coordinates:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{g} = -2 \\mathrm{d} U\\otimes \\mathrm{d} V -2 \\mathrm{d} V\\otimes \\mathrm{d} U + \\sin\\left(-U + V\\right)^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin\\left(-U + V\\right)^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "gt = -2 dU*dV - 2 dV*dU + sin(-U + V)^2 dth*dth + sin(-U + V)^2*sin(th)^2 dph*dph" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display(XNC.frame(), XNC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In terms of the non-compactified null coordinates $(u,v,\\theta,\\phi)$:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{g} = \\left( -\\frac{2}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} u\\otimes \\mathrm{d} v + \\left( -\\frac{2}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} v\\otimes \\mathrm{d} u + \\left( \\frac{u^{2} - 2 \\, u v + v^{2}}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{u^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, u v \\sin\\left({\\theta}\\right)^{2} + v^{2} \\sin\\left({\\theta}\\right)^{2}}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "gt = -2/((u^2 + 1)*v^2 + u^2 + 1) du*dv - 2/((u^2 + 1)*v^2 + u^2 + 1) dv*du + (u^2 - 2*u*v + v^2)/((u^2 + 1)*v^2 + u^2 + 1) dth*dth + (u^2*sin(th)^2 - 2*u*v*sin(th)^2 + v^2*sin(th)^2)/((u^2 + 1)*v^2 + u^2 + 1) dph*dph" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display(XN.frame(), XN)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and in terms of the default coordinates $(t,r,\\theta,\\phi)$:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{g} = \\left( -\\frac{4}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( \\frac{4}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( \\frac{4 \\, r^{2}}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{4 \\, r^{2} \\sin\\left({\\theta}\\right)^{2}}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "gt = -4/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1) dt*dt + 4/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1) dr*dr + 4*r^2/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1) dth*dth + 4*r^2*sin(th)^2/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1) dph*dph" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Einstein cylinder coordinates\n", "\n", "Let us introduce some coordinates $(\\tau,\\chi)$ such that the null coordinates $(U,V)$ are\n", "respectively half the retarded time $\\tau -\\chi$ and half the advanced time $\\tau+\\chi$:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,({\\tau}, {\\chi}, {\\theta}, {\\phi})\\right)$$" ], "text/plain": [ "Chart (M, (tau, ch, th, ph))" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC. = M.chart(r'tau:(-pi,pi):\\tau ch:(0,pi):\\chi th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "XC.add_restrictions([tauch-pi])\n", "XC" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\pi , \\pi \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$$" ], "text/plain": [ "tau: (-pi, pi); ch: (0, pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC.coord_range()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} U & = & -\\frac{1}{2} \\, {\\chi} + \\frac{1}{2} \\, {\\tau} \\\\ V & = & \\frac{1}{2} \\, {\\chi} + \\frac{1}{2} \\, {\\tau} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "U = -1/2*ch + 1/2*tau\n", "V = 1/2*ch + 1/2*tau\n", "th = th\n", "ph = ph" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XNC = XC.transition_map(XNC, [(tau-ch)/2, (tau+ch)/2, th, ph])\n", "XC_to_XNC.display()" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & U + V \\\\ {\\chi} & = & -U + V \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "tau = U + V\n", "ch = -U + V\n", "th = th\n", "ph = ph" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XNC.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The conformal metric takes then the form of the standard metric on the Einstein cylinder\n", "$\\mathbb{R}\\times\\mathbb{S}^3$:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\tilde{g} = -\\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau}+\\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\sin\\left({\\chi}\\right)^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "gt = -dtau*dtau + dch*dch + sin(ch)^2 dth*dth + sin(ch)^2*sin(th)^2 dph*dph" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display(XC.frame(), XC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The square of the conformal factor expressed in all the coordinates introduced so far:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} {\\Omega}^{ 2 } : & M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{4}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{4}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2} \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 4 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{4} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{4} - 8 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} + 4 \\, \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{4} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{4} \\end{array}$$" ], "text/plain": [ "Omega^2: M --> R\n", " (t, r, th, ph) |--> 4/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1)\n", " (u, v, th, ph) |--> 4/((u^2 + 1)*v^2 + u^2 + 1)\n", " (U, V, th, ph) |--> 4*cos(U)^2*cos(V)^2\n", " (tau, ch, th, ph) |--> 4*cos(1/2*ch)^4*cos(1/2*tau)^4 - 8*cos(1/2*ch)^2*cos(1/2*tau)^2*sin(1/2*ch)^2*sin(1/2*tau)^2 + 4*sin(1/2*ch)^4*sin(1/2*tau)^4" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(Omega^2).display()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\tau} & = & \\arctan\\left(r + t\\right) + \\arctan\\left(-r + t\\right) \\\\ {\\chi} & = & \\arctan\\left(r + t\\right) - \\arctan\\left(-r + t\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "tau = arctan(r + t) + arctan(-r + t)\n", "ch = arctan(r + t) - arctan(-r + t)\n", "th = th\n", "ph = ph" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XC = M.coord_change(XNC,XC) * M.coord_change(XN, XNC) * M.coord_change(XS, XN)\n", "XS_to_XC.display()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & \\frac{\\cos\\left(\\frac{1}{2} \\, {\\tau}\\right) \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)}{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}} \\\\ r & = & \\frac{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right) \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)}{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "t = cos(1/2*tau)*sin(1/2*tau)/(cos(1/2*ch)^2*cos(1/2*tau)^2 - sin(1/2*ch)^2*sin(1/2*tau)^2)\n", "r = cos(1/2*ch)*sin(1/2*ch)/(cos(1/2*ch)^2*cos(1/2*tau)^2 - sin(1/2*ch)^2*sin(1/2*tau)^2)\n", "th = th\n", "ph = ph" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XS = M.coord_change(XN, XS) * M.coord_change(XNC, XN) * M.coord_change(XC,XNC)\n", "XC_to_XS.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expressions for $t$ and $r$ can be simplified:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\cos\\left(\\frac{1}{2} \\, {\\tau}\\right) \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)}{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}}$$" ], "text/plain": [ "cos(1/2*tau)*sin(1/2*tau)/(cos(1/2*ch)^2*cos(1/2*tau)^2 - sin(1/2*ch)^2*sin(1/2*tau)^2)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tc = XC_to_XS(tau,ch,th,ph)[0]\n", "tc" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)}$$" ], "text/plain": [ "sin(tau)/(cos(ch) + cos(tau))" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tc.reduce_trig()" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right) \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)}{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}}$$" ], "text/plain": [ "cos(1/2*ch)*sin(1/2*ch)/(cos(1/2*ch)^2*cos(1/2*tau)^2 - sin(1/2*ch)^2*sin(1/2*tau)^2)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rc = XC_to_XS(tau,ch,th,ph)[1]\n", "rc" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)}$$" ], "text/plain": [ "sin(ch)/(cos(ch) + cos(tau))" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rc.reduce_trig()" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " t == t *passed*\n", " r == r *passed*\n", " th == th *passed*\n", " ph == ph *passed*\n", " tau == arctan((sin(ch) + sin(tau))/(cos(ch) + cos(tau))) + arctan(-(sin(ch) - sin(tau))/(cos(ch) + cos(tau))) **failed**\n", " ch == arctan((sin(ch) + sin(tau))/(cos(ch) + cos(tau))) - arctan(-(sin(ch) - sin(tau))/(cos(ch) + cos(tau))) **failed**\n", " th == th *passed*\n", " ph == ph *passed*\n", "NB: a failed report can reflect a mere lack of simplification.\n" ] } ], "source": [ "XS_to_XC.set_inverse(tc.reduce_trig(), rc.reduce_trig(), th, ph)\n", "XC_to_XS = XS_to_XC.inverse()" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & \\frac{\\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)} \\\\ r & = & \\frac{\\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "t = sin(tau)/(cos(ch) + cos(tau))\n", "r = sin(ch)/(cos(ch) + cos(tau))\n", "th = th\n", "ph = ph" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XS.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conformal Penrose diagram\n", "\n", "Let us draw the coordinate grid $(t,r)$ in terms of the coordinates $(\\tau,\\chi)$:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 112 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphXS = XS.plot(XC, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " max_range=30, number_values=51, plot_points=250, \n", " color={t: 'red', r: 'grey'})\n", "graph_i0 = circle((pi,0), 0.05, fill=True, color='grey') + \\\n", " text(r\"$i^0$\", (3.3, 0.2), fontsize=18, color='grey') \n", "graph_ip = circle((0,pi), 0.05, fill=True, color='red') + \\\n", " text(r\"$i^+$\", (0.25, 3.3), fontsize=18, color='red')\n", "graph_im = circle((0,-pi), 0.05, fill=True, color='red') + \\\n", " text(r\"$i^-$\", (0.25, -3.3), fontsize=18, color='red')\n", "graph_Ip = line([(0,pi), (pi,0)], color='green', thickness=2) + \\\n", " text(r\"$\\mathscr{I}^+$\", (1.8, 1.8), fontsize=18, color='green')\n", "graph_Im = line([(0,-pi), (pi,0)], color='green', thickness=2) + \\\n", " text(r\"$\\mathscr{I}^-$\", (1.8, -1.8), fontsize=18, color='green')\n", "graph = graphXS + graph_i0 + graph_ip + graph_im + graph_Ip + graph_Im\n", "show(graph, figsize=8)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "graph.save('glo_conf_diag_Mink.pdf', figsize=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some blow-up near $i^0$:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 84 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = XS.plot(XC, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " max_range=100, number_values=41, plot_points=200, \n", " color={t: 'red', r: 'grey'})\n", "graph += circle((pi,0), 0.005, fill=True, color='grey') + \\\n", " text(r\"$i^0$\", (pi, 0.02), fontsize=18, color='grey') \n", "show(graph, xmin=3., xmax=3.2, ymin=-0.2, ymax=0.2, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To produce a more satisfactory figure, let us use some logarithmic radial coordinate:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,(t, {\\rho}, {\\theta}, {\\phi})\\right)$$" ], "text/plain": [ "Chart (M, (t, rh, th, ph))" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XL. = M.chart(r't rh:\\rho th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "XL" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & t \\\\ {\\rho} & = & \\log\\left(r\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "t = t\n", "rh = log(r)\n", "th = th\n", "ph = ph" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XL = XS.transition_map(XL, [t, ln(r), th, ph])\n", "XS_to_XL.display()" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & t \\\\ r & = & e^{{\\rho}} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$$" ], "text/plain": [ "t = t\n", "r = e^rh\n", "th = th\n", "ph = ph" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XL.inverse().display()" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "XL_to_XC = M.coord_change(XS, XC) * M.coord_change(XL, XS)\n", "XC_to_XL = M.coord_change(XS, XL) * M.coord_change(XC, XS)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 40 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = XL.plot(XC, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " ranges={t: (-20, 20), rh: (-2, 10)}, number_values=19, \n", " color={t: 'red', rh: 'grey'})\n", "graph += circle((pi,0), 0.005, fill=True, color='grey') + \\\n", " text(r\"$i^0$\", (pi, 0.02), fontsize=18, color='grey') \n", "show(graph, xmin=3., xmax=3.2, ymin=-0.2, ymax=0.2, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Null radial geodesics in the conformal diagram\n", "\n", "To get a view of the null radial geodesics in the conformal diagram, it suffices to plot the chart $(u,v,\\theta,\\phi)$ in terms of the chart $(\\tau,\\chi,\\theta,\\phi)$. \n", "The following plot shows \n", "- the null geodesics defined by $(u,\\theta,\\phi) = (u_0, \\pi/2,\\pi)$ for 17 values of $u_0$ evenly spaced in $[-8,8]$ (dashed lines) \n", "- the null geodesics defined by $(v,\\theta,\\phi) = (v_0, \\pi/2,\\pi)$ for 17 values of $v_0$ evenly spaced in $[-8,8]$ (solid lines)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 42 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphXN = XN.plot(XC, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " number_values=17, plot_points=150, color='green', \n", " style={u: '--', v: '-'}, thickness=1.5)\n", "graph = graphXN + graph_i0 + graph_ip + graph_im + graph_Ip + graph_Im\n", "show(graph, figsize=8)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "graph.save('glo_conf_Mink_null.pdf', figsize=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conformal factor\n", "\n", "The conformal factor expressed in various coordinate systems:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{u^{2} + 1} \\sqrt{v^{2} + 1}} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - 2 \\, \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} \\\\ & \\left(t, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{t^{2} + 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1} \\sqrt{t^{2} - 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1}} \\end{array}$$" ], "text/plain": [ "Omega: M --> R\n", " (t, r, th, ph) |--> 2/(sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1))\n", " (u, v, th, ph) |--> 2/(sqrt(u^2 + 1)*sqrt(v^2 + 1))\n", " (U, V, th, ph) |--> 2*cos(U)*cos(V)\n", " (tau, ch, th, ph) |--> 2*cos(1/2*ch)^2*cos(1/2*tau)^2 - 2*sin(1/2*ch)^2*sin(1/2*tau)^2\n", " (t, rh, th, ph) |--> 2/(sqrt(t^2 + 2*t*e^rh + e^(2*rh) + 1)*sqrt(t^2 - 2*t*e^rh + e^(2*rh) + 1))" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression in terms of $(\\tau,\\chi,\\theta,\\phi)$ can be simplified:" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - 2 \\, \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}$$" ], "text/plain": [ "2*cos(1/2*ch)^2*cos(1/2*tau)^2 - 2*sin(1/2*ch)^2*sin(1/2*tau)^2" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.expr(XC)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = Omega.expr(XC) - cos(tau) - cos(ch)\n", "s.trig_reduce()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence we set" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{u^{2} + 1} \\sqrt{v^{2} + 1}} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right) \\\\ & \\left(t, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{t^{2} + 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1} \\sqrt{t^{2} - 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1}} \\end{array}$$" ], "text/plain": [ "Omega: M --> R\n", " (t, r, th, ph) |--> 2/(sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1))\n", " (u, v, th, ph) |--> 2/(sqrt(u^2 + 1)*sqrt(v^2 + 1))\n", " (U, V, th, ph) |--> 2*cos(U)*cos(V)\n", " (tau, ch, th, ph) |--> cos(ch) + cos(tau)\n", " (t, rh, th, ph) |--> 2/(sqrt(t^2 + 2*t*e^rh + e^(2*rh) + 1)*sqrt(t^2 - 2*t*e^rh + e^(2*rh) + 1))" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.add_expr(cos(tau) + cos(ch), XC)\n", "Omega.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A plot of $\\Omega$ in terms of the coordinates $(\\tau,\\chi)$:" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = plot3d(Omega.expr(XC), (tau,-pi,pi), (ch,0,pi)) \\\n", " + plot3d(0, (tau,-pi,pi), (ch,0,pi), color='yellow', opacity=0.7)\n", "show(graph, aspect_ratio=1, axes_labels=['tau', 'chi', 'Omega'])" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph, aspect_ratio=1, viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Differential of the conformal factor\n", "\n", "The 1-form $\\mathrm{d}\\Omega$ is:" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form dOmega on the 4-dimensional differentiable manifold M\n" ] } ], "source": [ "dOmega = Omega.differential()\n", "print(dOmega)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\Omega = \\left( -\\frac{4 \\, {\\left(t^{3} - {\\left(r^{2} - 1\\right)} t\\right)} \\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}}{r^{8} + t^{8} - 4 \\, {\\left(r^{2} - 1\\right)} t^{6} + 4 \\, r^{6} + 2 \\, {\\left(3 \\, r^{4} - 2 \\, r^{2} + 3\\right)} t^{4} + 6 \\, r^{4} - 4 \\, {\\left(r^{6} + r^{4} - r^{2} - 1\\right)} t^{2} + 4 \\, r^{2} + 1} \\right) \\mathrm{d} t + \\left( -\\frac{4 \\, {\\left(r^{3} - r t^{2} + r\\right)} \\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}}{r^{8} + t^{8} - 4 \\, {\\left(r^{2} - 1\\right)} t^{6} + 4 \\, r^{6} + 2 \\, {\\left(3 \\, r^{4} - 2 \\, r^{2} + 3\\right)} t^{4} + 6 \\, r^{4} - 4 \\, {\\left(r^{6} + r^{4} - r^{2} - 1\\right)} t^{2} + 4 \\, r^{2} + 1} \\right) \\mathrm{d} r$$" ], "text/plain": [ "dOmega = -4*(t^3 - (r^2 - 1)*t)*sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1)/(r^8 + t^8 - 4*(r^2 - 1)*t^6 + 4*r^6 + 2*(3*r^4 - 2*r^2 + 3)*t^4 + 6*r^4 - 4*(r^6 + r^4 - r^2 - 1)*t^2 + 4*r^2 + 1) dt - 4*(r^3 - r*t^2 + r)*sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1)/(r^8 + t^8 - 4*(r^2 - 1)*t^6 + 4*r^6 + 2*(3*r^4 - 2*r^2 + 3)*t^4 + 6*r^4 - 4*(r^6 + r^4 - r^2 - 1)*t^2 + 4*r^2 + 1) dr" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega.display()" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\Omega = -2 \\, \\cos\\left(V\\right) \\sin\\left(U\\right) \\mathrm{d} U -2 \\, \\cos\\left(U\\right) \\sin\\left(V\\right) \\mathrm{d} V$$" ], "text/plain": [ "dOmega = -2*cos(V)*sin(U) dU - 2*cos(U)*sin(V) dV" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega.display(XNC.frame(), XNC)" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "M.set_default_chart(XNC)\n", "M.set_default_frame(XNC.frame())" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\Omega = -2 \\, \\cos\\left(V\\right) \\sin\\left(U\\right) \\mathrm{d} U -2 \\, \\cos\\left(U\\right) \\sin\\left(V\\right) \\mathrm{d} V$$" ], "text/plain": [ "dOmega = -2*cos(V)*sin(U) dU - 2*cos(U)*sin(V) dV" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega.display()" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-2 \\, \\cos\\left(V\\right) \\sin\\left(U\\right) \\mathrm{d} U -2 \\, \\cos\\left(U\\right) \\sin\\left(V\\right) \\mathrm{d} V$$" ], "text/plain": [ "-2*cos(V)*sin(U) dU - 2*cos(U)*sin(V) dV" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega1 = M.one_form()\n", "dOmega1[0] = -2*cos(V)*sin(U)\n", "dOmega1[1] = -2*cos(U)*sin(V)\n", "dOmega1.display()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-2 \\, \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right) \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right) \\mathrm{d} {\\tau} -2 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right) \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right) \\mathrm{d} {\\chi}$$" ], "text/plain": [ "-2*cos(1/2*tau)*sin(1/2*tau) dtau - 2*cos(1/2*ch)*sin(1/2*ch) dch" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega1.display(XC.frame(), XC)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Einstein static universe" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional differentiable manifold E\n" ] } ], "source": [ "E = Manifold(4, 'E')\n", "print(E)" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(E,({\\tau}, {\\chi}, {\\theta}, {\\phi})\\right)$$" ], "text/plain": [ "Chart (E, (tau, ch, th, ph))" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XE. = E.chart(r'tau:\\tau ch:(0,pi):\\chi th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "XE" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$$" ], "text/plain": [ "tau: (-oo, +oo); ch: (0, pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XE.coord_range()" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\tau} :\\ \\left( -\\pi , \\pi \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$$" ], "text/plain": [ "tau: (-pi, pi); ch: (0, pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Embedding of $M$ in $E$" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Differentiable map Phi from the 4-dimensional differentiable manifold M to the 4-dimensional differentiable manifold E\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi:& M & \\longrightarrow & E \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arctan\\left(r + t\\right) + \\arctan\\left(-r + t\\right), \\arctan\\left(r + t\\right) - \\arctan\\left(-r + t\\right), {\\theta}, {\\phi}\\right) \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arctan\\left(u\\right) + \\arctan\\left(v\\right), -\\arctan\\left(u\\right) + \\arctan\\left(v\\right), {\\theta}, {\\phi}\\right) \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(U + V, -U + V, {\\theta}, {\\phi}\\right) \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) \\\\ & \\left(t, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arctan\\left(t + e^{{\\rho}}\\right) + \\arctan\\left(t - e^{{\\rho}}\\right), \\arctan\\left(t + e^{{\\rho}}\\right) - \\arctan\\left(t - e^{{\\rho}}\\right), {\\theta}, {\\phi}\\right) \\end{array}$$" ], "text/plain": [ "Phi: M --> E\n", " (t, r, th, ph) |--> (tau, ch, th, ph) = (arctan(r + t) + arctan(-r + t), arctan(r + t) - arctan(-r + t), th, ph)\n", " (u, v, th, ph) |--> (tau, ch, th, ph) = (arctan(u) + arctan(v), -arctan(u) + arctan(v), th, ph)\n", " (U, V, th, ph) |--> (tau, ch, th, ph) = (U + V, -U + V, th, ph)\n", " (tau, ch, th, ph) |--> (tau, ch, th, ph) = (tau, ch, th, ph)\n", " (t, rh, th, ph) |--> (tau, ch, th, ph) = (arctan(t + e^rh) + arctan(t - e^rh), arctan(t + e^rh) - arctan(t - e^rh), th, ph)" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi = M.diff_map(E, {(XC, XE): [tau, ch, th, ph]},\n", " name='Phi', latex_name=r'\\Phi')\n", "print(Phi)\n", "Phi.display()" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 18 graphics primitives" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.plot(XE, mapping=Phi, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " plot_points=200, color={t: 'red', r: 'grey'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Embedding of $E$ in $\\mathbb{R}^5$" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5-dimensional differentiable manifold R^5\n" ] } ], "source": [ "R5 = Manifold(5, 'R^5', latex_name=r'\\mathbb{R}^5')\n", "print(R5)" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{R}^5,({\\tau}, W, X, Y, Z)\\right)$$" ], "text/plain": [ "Chart (R^5, (tau, W, X, Y, Z))" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X5. = R5.chart(r'tau:\\tau W X Y Z')\n", "X5" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Differentiable map Psi from the 4-dimensional differentiable manifold E to the 5-dimensional differentiable manifold R^5\n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Psi:& E & \\longrightarrow & \\mathbb{R}^5 \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, W, X, Y, Z\\right) = \\left({\\tau}, \\cos\\left({\\chi}\\right), \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)\\right) \\end{array}$$" ], "text/plain": [ "Psi: E --> R^5\n", " (tau, ch, th, ph) |--> (tau, W, X, Y, Z) = (tau, cos(ch), cos(ph)*sin(ch)*sin(th), sin(ch)*sin(ph)*sin(th), cos(th)*sin(ch))" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Psi = E.diff_map(R5, {(XE, X5): [tau,\n", " cos(ch),\n", " sin(ch)*sin(th)*cos(ph), \n", " sin(ch)*sin(th)*sin(ph), \n", " sin(ch)*cos(th)]},\n", " name='Psi', latex_name=r'\\Psi')\n", "print(Psi)\n", "Psi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Einstein cylinder:" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "