{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Conformal completion of Minkowski spacetime\n", "\n", "This Jupyter/SageMath worksheet is relative to the lectures\n", "[Geometry and physics of black holes](http://luth.obspm.fr/~luthier/gourgoulhon/bh16/)\n", " \n", "These computations are based on [SageManifolds](http://sagemanifolds.obspm.fr) (version 1.0, as included in SageMath 7.5 and higher versions)\n", "\n", "The worksheet file (ipynb format) can be downloaded from [here](https://raw.githubusercontent.com/egourgoulhon/BHLectures/master/sage/conformal_Minkowski.ipynb)." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "*NB:* a version of SageMath at least equal to 7.5 is required to run this worksheet: " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.0.beta6, Release Date: 2017-05-12'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We also define a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "viewer3D = 'threejs' # must be 'threejs', jmol', 'tachyon' or None (default)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Spherical coordinates on Minkowski spacetime\n", "\n", "We declare the spacetime manifold $M$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "and the spherical coordinates $(t,r,\\theta,\\phi)$ as a chart on $M$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (t, r, th, ph))" ] }, "execution_count": 5, "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": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t: (-oo, +oo); r: (0, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.coord_range()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "In term of these coordinates, the Minkowski metric is" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = -dt*dt + dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 7, "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": { "deletable": true, "editable": true }, "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": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (u, v, th, ph))" ] }, "execution_count": 8, "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": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "u: (-oo, +oo); v: (-oo, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN.coord_range()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "u = -r + t\n", "v = r + t\n", "th = th\n", "ph = ph" ] }, "execution_count": 10, "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": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XN.inverse().display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "In terms of the null coordinates $(u,v,\\theta,\\phi)$, the Minkowski metric writes" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(XN.frame(), XN)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Let us plot the coordinate grid $(u,v)$ in terms of the coordinates $(t,r)$:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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SIPRaqF41Z0v3EpvbM1RpVPjz0p96+ZZIELCuZ1jfuz4iJ0ZiYf+FFkkQ4J4hw1iC1SKc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"text/plain": [ "Graphics object consisting of 33 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "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={u: 1, v: 2})\n", "show(graph)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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zboeEpQk49PohmnwrUjQ8ZAA1h4qifaM1dgG1NLNEXOM4msMiUTWHiqJ8ojTa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arLVazjiA+LxWGaW1yuJdACdOKw5+we7o0db4i+SBitnCsOKpWKS69OF30RKVqAThwaVY1MxpcW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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, fontsize=16)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save(\"glo_null_coord.pdf\", xmin=0, xmax=4, ymin=0, ymax=4, aspect_ratio=1, fontsize=16)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"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": 17, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save('glo_atan.pdf', aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (U, V, th, ph))" ] }, "execution_count": 18, "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": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XNC.coord_range()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "U = arctan(u)\n", "V = arctan(v)\n", "th = th\n", "ph = ph" ] }, "execution_count": 20, "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": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "u = tan(U)\n", "v = tan(V)\n", "th = th\n", "ph = ph" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN_to_XNC.inverse().display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Expressed in terms of the coordinates $(U,V,\\theta,\\phi)$, the metric tensor is" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(XNC.frame(), XNC)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Let us call $\\Omega^{-2}$ the common factor: " ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 23, "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": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.display(XS)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Conformal metric\n", "\n", "We introduce the metric $\\tilde g = \\Omega^2 g$:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 25, "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": { "deletable": true, "editable": true }, "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": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g22 = gt[XNC.frame(), 2, 2, XNC].expr()\n", "g22" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sin(-U + V)^2" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g22.factor().reduce_trig()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g33st = gt[XNC.frame(), 3, 3, XNC].expr() / sin(th)^2\n", "g33st" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sin(-U + V)^2" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g33st.factor().reduce_trig()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "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": { "deletable": true, "editable": true }, "source": [ "Hence the final form of the conformal metric in terms of the compactified null coordinates:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display(XNC.frame(), XNC)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "In terms of the non-compactified null coordinates $(u,v,\\theta,\\phi)$:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display(XN.frame(), XN)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "and in terms of the default coordinates $(t,r,\\theta,\\phi)$:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": 34, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (tau, ch, th, ph))" ] }, "execution_count": 34, "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": 35, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "tau: (-pi, pi); ch: (0, pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC.coord_range()" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 36, "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": 37, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "tau = U + V\n", "ch = -U + V\n", "th = th\n", "ph = ph" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XNC.inverse().display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": 38, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "gt = -dtau*dtau + dch*dch + sin(ch)^2 dth*dth + sin(ch)^2*sin(th)^2 dph*dph" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display(XC.frame(), XC)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The square of the conformal factor expressed in all the coordinates introduced so far:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(Omega^2).display()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 40, "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": 41, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 41, "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": { "deletable": true, "editable": true }, "source": [ "The expressions for $t$ and $r$ can be simplified:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tc = XC_to_XS(tau,ch,th,ph)[0]\n", "tc" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sin(tau)/(cos(ch) + cos(tau))" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tc.reduce_trig()" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rc = XC_to_XS(tau,ch,th,ph)[1]\n", "rc" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sin(ch)/(cos(ch) + cos(tau))" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rc.reduce_trig()" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "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": 47, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XS.display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "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": 48, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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IEbi5w2DB6dMs/+UX4uzs6NWzJz5WVqL4rbk5zJtH+Oefs7VZMxokJtJ50SLC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"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, 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)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save('glo_conf_diag_Mink.pdf')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Some blow-up near $i^0$:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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1PpS1gwcT0q8f7dq1Y+PGjSQkJGC0s4Nt25SA7tcPsrLu3XBnUlD19tv0Tk2l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"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, 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": { "deletable": true, "editable": true }, "source": [ "To produce a more satisfactory figure, let us use some logarithmic radial coordinate:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (t, rh, th, ph))" ] }, "execution_count": 51, "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": 52, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t = t\n", "rh = log(r)\n", "th = th\n", "ph = ph" ] }, "execution_count": 52, "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": 53, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t = t\n", "r = e^rh\n", "th = th\n", "ph = ph" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XL.inverse().display()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "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": 55, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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LS1GpVA+1Y3Tnk97eXtRqNZ2dnfj7++t/kDg6OhIQFMT5qipK+vsJuHoVy4QE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"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": { "deletable": true, "editable": true }, "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": 56, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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X6eVcXDEqx8HIZHGlqAZTBeP8c/MJQaA5Z+bo5XwcjMpxMDIJnUOxsLCQbty4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\nwu/ABJGh6+iUKOrz9XFqyim4vOeCTm06aXs6TSYpLwkf/P0B4rPj1TL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E3Xd2J6FISKuC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"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={u: 1, v: 2})\n", "graph = graphXN + graph_i0 + graph_ip + graph_im + graph_Ip + graph_Im\n", "show(graph)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save('glo_conf_Mink_null.pdf')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Conformal factor\n", "\n", "The conformal factor expressed in various coordinate systems:" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The expression in terms of $(\\tau,\\chi,\\theta,\\phi)$ can be simplified:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.expr(XC)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = Omega.expr(XC) - cos(tau) - cos(ch)\n", "s.trig_reduce()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Hence we set" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.add_expr(cos(tau) + cos(ch), XC)\n", "Omega.display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "A plot of $\\Omega$ in terms of the coordinates $(\\tau,\\chi)$:" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "\n", "