{ "cells": [ { "cell_type": "markdown", "metadata": {}, "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) (v0.9)\n", "\n", "The worksheet file (ipynb format) can be downloaded from [here](https://raw.githubusercontent.com/egourgoulhon/BHLectures/master/sage/conformal_Minkowski.ipynb).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "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": 2, "metadata": { "collapsed": false }, "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": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (t, r, th, ph))" ] }, "execution_count": 3, "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": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t: (-oo, +oo); r: (0, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 4, "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": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = -dt*dt + dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 5, "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": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (u, v, th, ph))" ] }, "execution_count": 6, "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": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "u: (-oo, +oo); v: (-oo, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN.coord_range()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "u = -r + t\n", "v = r + t\n", "th = th\n", "ph = ph" ] }, "execution_count": 8, "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": 9, "metadata": { "collapsed": false }, "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": 9, "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": 10, "metadata": { "collapsed": false }, "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": 10, "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": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUIAAAJFCAYAAACoQP65AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niZDBYFR4mAgZDEaF5/8AonqMRSPCOysAAAAASUVORK5CYII=\n", "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}, nb_values=17,\n", " plot_points=200, color='green', style={u: '-', v: ':'}, thickness={u: 1, v: 2})\n", "show(graph)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAi0AAAJECAYAAADaEhTgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\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": 13, "metadata": { "collapsed": 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": {}, "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": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAw8AAAD0CAYAAADdYRqRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzt3Xl4FFW+xvG3QxBICCFASEIA2VcJYFiiLIoLIGJARUgc\nBnAUQVHcRtR7L3JnHPd7B3F0BEWuOKNER4FBGGU0sgkMA4yBKDsoWyDCkIWENUndP45JJyEJnaW7\n0t3fz/PUU13V1VW/QxOoN1V1jsOyLEsAAAAAcBkBdhcAAAAAwDsQHgAAAAC4hPAAAAAAwCWEBwAA\nAAAuITwAAAAAcAnhAQAAAIBLCA8AAAAAXEJ4AAAAAOASwgMAAAAAlxAeAAAAALiE8AAAPuLgwYOK\njY1VdHS0AgICFBAQoJYtW6p379769ttvi7b74osv1KZNm6JtGjdurBtvvNHGygEA3sJhWZZldxEA\ngJqzYcMGDRw4UEOGDFFycnK52917770qKCjQO++8o8DAQA9WCADwVvxvAQA+Zu3atXI4HBoxYkSF\n2+Xm5uqFF14gOAAAXMZtSwDgY1avXi1JGjJkSIXb/fDDD2rXrp0HKgIA+ArCAwD4kPz8fG3YsEGh\noaHq3bt3udvt2LFD3bt392BlAABfQHgAAB+yefNm5eTkaPDgwXI4HOVut2rVqstemQAAoDTCAwD4\nkNWrV8vhcFw2GKxevZrwAACoNMIDAPiQVatWSbr88w5HjhxRy5YtPVESAMCHEB4AwEfk5eVpw4YN\natKkiWJiYsrdLjU1VT169PBgZQAAX0F4AAAfsWXLFuXm5uq6666rcDuedwAAVBXhAQB8xLZt2yRJ\nAwcOrHC7FStWaOjQoZ4oCQDgYwgPAOAjsrKy5HA41KVLl3K32bRpk8LCwtS0aVMPVgYA8BUMKwoA\nPqJr166yLEvnz58v8/1///vfeuCBB7R06VIPVwYA8BVceQAAH3HLLbeoS5cu+vOf/3zJe8eOHdO4\nceP02muvqXXr1jZUBwDwBQ7Lsiy7iwAA1Iz9+/drzJgxatu2rcaOHSvLsrRhwwbt3r1br732mrp1\n62Z3iQAAL0Z4AAAflJycrG3btikwMFDXXHON+vbta3dJAAAfQHgAAAAA4BKeeQAAAADgEsIDAAAA\nAJcQHgAAAAC4hPAAAAAAwCWEBwAAAAAuITwAAAAAcAnhAQAAAIBLCA8AAAAAXEJ4AAAAAOASwgMA\nAAAAlxAeAAAAALiE8AAAAADAJYQHAPBxlmUpOztblmXZXQoAwMsRHgDAx50+fVqhoaE6ffq03aUA\nALwc4QEAAACASwLdfYBjx8xUnvr1pW7dKt7Hjh3SuXPlvx8VZabynD0r7dxZ8TG6dpUaNCj/fdrh\nRDsM2uFEO5wq245169bp1Vdf1datW3Xs2DF99NFStW8fX+7nt25doylThpRY53A4dOzYMTVv3rzM\nduTkmPkttyQoMDBQI0cm6sknE2u0HaV56/dRGu1woh1OtMOgHU410Q6vYbnZrFmWJZU/det2+X10\n61bxPmbNqvjz331X8eclsw3toB20g3Z4uh2ff/65NXPmTGvp0qVWQECA9Yc//PUy7VhtBQQEWPv2\n7bPS09OLporbkWVJ+nnO90E7aAftoB21sR3ewmFZluXOcEKidKIdBu1woh1OtEMKCAhw6crD1Kk3\nKCMjQ40aNSpzm0uvPGTruutCtWZNlho2bMT3UQztcKIdBu1woh1OXHlwcnt4AAC4JiAgQEuXLlV8\nfPnhYc2aNRoyZIjatGmjc+fO6aqrrtJ///d/69prry33M9nZ2QoNDVVWVla5gQMAAFfwwDQAeJGo\nqCjNmzdPn376qRYvXqxWrVrp+uuvV0pKit2lAQD8gNsfmAYA1JxOnTqpU6dORctxcXHav3+/Zs+e\nrYULF9pYGQDAHxAeAMDL9evXT+vXr7/sdh07dpTD4VB0dLSio6MlSYmJiUpMrLjnJQAAChEeAMDL\npaSkKKqipwF/tnfvXp55AABUC+EBAGyUm5urffv2qbDvigMHDmjbtm1q0qSJWrVqpWeeeUZpaWlF\ntyTNmTNHbdu2Vffu3XXu3Dm98847WrVqlb788ks7mwEA8BOEBwCw0ZYtWzRkyBA5HA45HA498cQT\nkqSJEydqwYIFOn78uA4fPly0/YULF/TEE08oLS1NQUFBiomJUXJysgYPHmxXEwAApeTnm+5jz583\n8+Kvo6Oln8f09Ep01QoAPo6uWgH4k4ICM3ZD4VTeSbw7X+fllV/fH/8oPfCA5/48ahpXHgAAAOBW\n+flSbq6Zzp6VzpxxntwXf13Re65ud/683a2tWEUD2nkDwgMA+ImEhAQFBgbSwxKAMhU/wc/Jcb4u\na6ro/bLeq+0n9FURGGhGjq5fX6pXz/XXPXrYXXn1cNsSAPg4blsCfJNlmd+0Z2dLp08758Vflzcv\n/rrwZN8bT/CDgqQGDcxU/HXhcv365nVlTu5deV2vnlSnjt2ttwdXHgAAADysoMCctGdmXn7Kzi4/\nGBQU2N2SSwUESMHBUsOGZl56Kuskv7zlit6rV09yOOxurf8hPAAAAFRBfr6UkSH9+9/OKSPDtUCQ\nlWX/iX9QkBQSUv5JflnrXdmWk3rfRngAAAB+zbLMA7fFQ0Dp6dSpS9dlZprPelJwsDnhDwmRGjUq\ne+7KuoYNzT37QGXx1wYA/AQPTMOfXLwonTgh/fSTlJ5u5oVT8eX0dOnkSc/0gBMYKDVu7PoUFiaF\nhpqT/cITfn+9zx61Bw9MA4CP44Fp+IqCAhMI0tKc07FjZQeCjAz31dG4sdS0adlTWJiZygoDQUHc\nzgPvx5UHAABgK8sytwUdPVoyGJSejh83zxnUlIAAKTzcTM2amZP/Jk3KDwaF4YDbfeDP+OsPAADc\n6sIF6cgR6dAh53TwYMnlM2dq5lgNG0rNm0sREWZeOBVfLnzdpIkJEABcR3gAAADVkpsr7d8v/fjj\npaHg0CFza1F1bpJ2OMwJf4sWZoqKKvk6IsJM4eHm1iAA7kN4AAAAFbIs86zB/v1lT+npVd93UJDU\nurXUqpWZCkNB8SkigluFgNqCH0UA8BP0toTLyc2V9uyRdu2Sdu408717TUA4fbpq+4yKMuGg9HTl\nlWbepAkPEQPehN6WAMDH0dsSirMs0yPRrl0lQ8KuXeaWo8qKjJQ6dJDat5fatXOGgtatpZYtzYBh\nAHwHVx4AAPBROTlSaqq0fbu0bZuZ79hRuW5M69SR2rQx4aD01K6dGbQMgP8gPAAA4OUsyzysXBgS\nCoPC/v2uP6gcGip16SJ17Wrmha/btpXq1nVr+QC8COEBAAAvYlnSvn3Sli3S5s1mvm2blJ3t2udb\ntjShoHRIiIjg2QMAl0d4AACgFjtxQtqwQfrHP0xY2LpVysy8/OcaNJB69JBiYqSePc3Uo4cZ6RgA\nqorwAAB+gt6Waj/Lknbvltavd0579lz+c61aOQNCz54mMHToYJ5XAICaRG9LAOBl1q1bp1dffVVb\nt27VsWPHtHTpUsXHx5e7Pb0t1V7nz0v//KczKGzYIJ06VfFnIiOlvn3N1KePmcLDPVMvAHDlAQC8\nTG5urnr16qV7771Xd9xxh93loBLy86Vvv5WSk830zTfS2bPlb1+3rhQbKw0YIF17rdS/vxQd7bl6\nAaA0wgMAeJnhw4dr+PDhkiQuHtdulmVuOyoMC6tWVdxNatOmJiQMGGCm2Fjz7AIA1BaEBwAAatDZ\ns9Lq1dKKFWb68cfyt23ZUrrhBmnwYBMWOnemxyMAtRvhAQCAajp8WPrb36Tly80VhvJuRQoLM2Hh\nxhvN1LEjYQGAdyE8AICf6NixoxwOh6KjoxX9843z9LxUdfv2SZ98Iv3lL9K//lX2NnXrmqsKQ4ea\nsNCrFz0gAfBuhAcA8BN79+6lt6Vq2rvXhIW//EVKSSl7m8hI6dZbzXTTTVJIiGdrBAB3IjwAAFCB\nvXuljz4ygWH79rK3iY2V4uNNYOjdWwoI8GyNAOAphAcA8DK5ubnat29fUU9LBw4c0LZt29SkSRO1\natXK5up8w6lTJjC8/74Z2bksfftKd90ljRkjtW3r2foAwC4MEgcAXmbNmjUaMmSIHKWetJ04caIW\nLFhwyfYMEuea/Hxp5Urp3Xelzz6TLl68dJv+/Z2B4corPV8jANiN8AAAPo7wULFjx0xgeOcd6dCh\nS9/v2VMaP14aO1Zq3drz9QFAbcJtSwDgJxISEhQYGEgPS5IKCkyXqnPnSsuWSXl5Jd+PjJR+8Qvp\nl7804QEAYHDlAQB8HFcenLKypPnzpbfekvbvL/mewyHdcos0daqZB/LrNQC4BP80AgB83oED0pw5\n0oIFUk5OyfciI6V775UmT+Y5BgC4HMIDAMBnbdsmvfii6Wa1oKDkezffLE2ZYrpYrVvXnvoAwNsQ\nHgAAPmf9ehMaVqwoub5BA2niROmRR6QuXeypDQC8GeEBAOAz1qyRnn1WWru25PrwcBMYpk6Vmja1\npzYA8AWEBwDwE77c29KWLdJ//qf097+XXN+6tfTkk9KvfiUFBdlTGwD4EnpbAgAf58u9Le3YIc2c\nKS1eXHJ9587SM89Id9/N8wwAUJO48gAA8Do//ijNmiX9+c8lH4Ru00b6zW/MGA116thVHQD4LsID\nAMBr5OZKL70kvfqqdP68c31kpLkCcd990hVX2FcfAPg6wgMAoNazLOnjj6Vf/1o6csS5PixMevpp\n6aGHeKYBADyB8AAAqNW2bZOmTy/Zg1Lduqb3pP/6Lyk01L7aAMDfBNhdAADAMxISEhQfH69FixbZ\nXYpLTp2Spk2Trr66ZHAYPlxKTTW3LhEcAMCz6G0JAHycN/a29MknJjj89JNzXfv20muvSbfeKjkc\n9tUGAP6MKw8AgFojPV0aM0a66y5ncAgONqNFf/+9NHIkwQEA7MQzDwAA21mW9MEH5jmGU6ec60eN\nkt58U4qOtq82AIAT4QEAYKsjR6SpU6UVK5zrmjWT3nhDGjuWKw0AUJtw2xIAwBaWJS1cKHXvXjI4\nJCSYkaPHjSM4AEBtQ3gAAJu9+eabatu2rRo0aKC4uDht3ry53G3XrFmjgICAElOdOnX0U/Eni8tR\nm3pbysyUEhOlSZOk7GyzLjJSWrJEWrRICg+3tTwAQDm4bQkAbPTRRx/piSee0Ntvv61+/fpp9uzZ\nGjZsmPbs2aNmzZqV+RmHw6E9e/YoJCSkaF3z5s0ve6ykpKRa0dvSN99Iv/iFdOiQc92ECaYnpbAw\n++oCAFweVx4AwEazZ8/WlClTNGHCBHXp0kVz585VUFCQFixYUOHnwsPD1bx586LJG+TnS7NmSddd\n5wwOjRubkaMXLiQ4AIA3IDwAgE0uXryorVu36sYbbyxa53A4dNNNN2njxo3lfs6yLPXq1UstWrTQ\n0KFDtWHDBk+UWy0nTpjB3X77W6mgwKwbPFjavt10ywoA8A6EBwCwycmTJ5Wfn6+IiIgS6yMiInT8\n+PEyPxMVFaV58+bp008/1eLFi9WqVStdf/31SklJ8UTJVfLPf0qxsdJXX5nlOnWk55+Xvv5aatXK\n3toAAJXDMw8A4EU6deqkTp06FS3HxcVp//79mj17thYuXGhjZZeyLOntt6Xp06ULF8y6iAhzm9Lg\nwfbWBgCoGsIDANikWbNmqlOnjtLT00usT09PV2RkpMv76devn9avX3/Z7Tp27CiHw6Ho6GhF/zzq\nWmJiohITEytXuAvOnpUefFB67z3nugEDTHBo0aLGDwcA8BDCAwDYpG7duoqNjVVycrLi4+MlmecZ\nkpOTNX36dJf3k5KSoqioqMtut3fvXo/0tnTggHTnnVLxO6keeUR69VWpbl23Hx4A4EaEBwCw0eOP\nP65JkyYpNja2qKvWM2fOaNKkSZKkZ555RmlpaUW3JM2ZM0dt27ZV9+7dde7cOb3zzjtatWqVvvzy\nSxtb4ZScbB6Azsgwy0FB0vz5ZkwHAID3IzwAgI3Gjh2rkydP6tlnn1V6erp69eqllStXKvznUdKO\nHz+uw4cPF21/4cIFPfHEE0pLS1NQUJBiYmKUnJyswbXgIYJ586Rp00yXrJLUqZO0eLEZQRoA4Bsc\nlmVZdhcBAHCf7OxshYaGKisryy23LeXnS7/+tRnkrdDIkdKf/yyFhtb44QAANqKrVgBAlWVnS6NG\nlQwOTzwhLV1KcAAAX8RtSwDgJxISEhQYGFhjPSwdOSKNGCGlpprlwEDpj3+UJk+u9q4BALUUty0B\ngI9zx21LqanSLbdIR4+a5bAw6dNPpSFDamT3AIBaiisPAIBK+fpr6fbbzS1LktSunfT55+YBaQCA\nb+OZBwCAyz75RBo+3Bkc+vaVNm4kOACAvyA8AABc8u670rhx0sWLZnnkSGnVKql5c3vrAgB4DuEB\nAHBZr74q3XefVFBglidNkpYskYKDbS0LAOBhhAcA8BMJCQmKj4/XokWLXP6MZUnPPCPNmOFc9/jj\n5ipEIE/NAYDfobclAPBxVe1tKT9fevBB6e23neuef96ECYfDDYUCAGo9fm8EALjEhQvSL38pffyx\nWXY4pDfflB54wN66AAD2IjwAAErIzZXuvFNaudIsBwZKf/qTlJBgb10AAPsRHgAARU6flm69VVq3\nziw3aGC6Zx0xwt66AAC1A+EBACDJjN1wyy3Shg1mOTRUWr5cGjjQ3roAALUHvS0BgJ+oqLelrCxp\n6FBncAgLMyNJExwAAMXR2xIA+LjL9baUkSENGyZt3myWmzaVvvpK6tXLw4UCAGo9rjwAgB87dUq6\n6SZncAgPN6NGExwAwLudPXtWDz/8sH7xi1/o5ptvVk5OTon358yZo379+lV6vzzzAAB+6uRJ6eab\npZQUs9y8ublVqXt3e+sCAFTfc889p0cffVRRUVFq2LChFi5cqGnTphW9P3/+fFXlBiSuPACAHzpx\nQrrhBmdwiIyUVq8mOACALzh58qQuXLig9u3ba/369ZKk5s2bF71/6tQp7dixQzfccEOl9+328FDW\ng3nwDXy3vonv1XcVPjA9d+4iDRkipaaa9VFRJjh07WpreagCfl59F9+tb/LU93r06FH96le/kiS9\n//77Cg0N1ciRI4veX7t2rSzL0vXXX1/pfRMeUGV8t76J79V3JSUlad68ZZozJ1Hff2/WRUdLa9ZI\nnTvbWxuqhp9X38V365s89b327NlT3bp107lz57R06VKNGzdODRo0KHp/zZo1CggIqJ3hAQBQO6Sl\nSddfL+3aZZZbtTLBoWNHW8sCALjJF198oTNnzmjMmDEl1q9bt05XXXWVmjRpUul9+mx4sCOx2/Vb\nAn/67YQ//RnzvXLcmnbrrdKePeb1lVea4NC+vXuP6U8/O/zM+uZx+V5987j+8r1u2bJFderU0aBB\ng4rWnT59WikpKUXPO3zyySfKzc11eZ+EBy8/pp3HtYM//RnzvXLcmnL4sJkfOGDmbdua4NC2rfuP\n7U8/O/zM+uZx+V5987j+8r1mZWUpPDxc9erVK1qXnJysgoICDfx5FNDFixcrODjY5X261FWrZVk6\nffp0Jcs18vLylJ2dXaXPVocdx/Wnttp1XNrqm8f1p7Z6+riHDkkjRhQeK1tt20rLl5sRpD1RAn+f\nfO+Y/nZc2uqbx/XGtoaEhMjhcFTqM3FxcZo/f76ys7PVqFEjHT58WH/4wx/kcDgUFRWl/fv368or\nr6zUPl0aYbpwdFIAAAAAnpeVlaVGjRpV+nMzZ87U5s2b1bZtW9WrV0+//e1v9dJLL2nz5s1q2bKl\nXn/9dYWEhLi8P5fCQ3WuPAAAPO+HH6SRI6UjRyQpW1IrbdlyWB07Vv4/HgCA/apy5cEdXAoPAADv\nsX+/NGSI81mHjh2ztXdvaJV/awUAQCGffWAaAPzRvn2mO9bC4NCtm7Riha0lAQB8iEsPTAMAar+9\ne01wSEszy927S8nJUrFxgQAAqBauPACAD9i9W7ruOmdw6NFD+vprKSLC3roAAL6F8AAAXm7XLnPF\n4dgxsxwTY644NG9ecruEhATFx8f7Tf/mAICa5/bwsHPnTo0aNUqNGzdWw4YN1b9/fx0x3X/AB0yd\nOlUBAQF6/fXX7S4F1ZSXl6ennnpKMTExatiwoaKjozVx4kQdKzwjRa20c6cJDsePm+WePU1wCA+/\ndNukpCQtW7ZMiYmJHq0RNevFF19Uv3791KhRI0VEROj222/XnsKhw+EzXnrpJQUEBOjxxx+3uxTU\ngLS0NP3yl79Us2bNFBQUpJ49e+pf//qX3WVViVvDw/79+zVo0CB169ZNa9euVWpqqmbOnKn69eu7\n87DwkCVLlmjTpk2Kjo62uxTUgDNnziglJUWzZs3St99+qyVLlmj37t0aNWqU3aWhHN9/b4JDerpZ\n7t3bBIdmzWwtC262bt06Pfzww9q0aZO++uorXbx4UUOHDtXZs2ftLg01ZPPmzXr77bfVs2dPu0tB\nDcjMzNSAAQNUr149rVy5Ujt37tT//u//KiwszO7SqsStXbUmJibqiiuu0MKFC911CNjk6NGjuuaa\na7Ry5UqNGDFCjz32mKZPn253WahhW7ZsUf/+/XXw4EG1bNnS7nJQzPbt0k03SSdOmOWrr5a+/FJq\n0uTSbQsH+qSrVt908uRJNW/eXGvXrtXAgQPtLgfVlJOTo9jYWL311lt67rnn1Lt3b/3+97+3uyxU\nw9NPP62NGzdqzZo1dpdSI9x25cGyLK1YsUIdO3bU8OHDFRERobi4OP31r3911yHhIZZlacKECZox\nY4a6du1qdzlwo8zMTDkcDjVu3NjuUlDMP/5hHo4uDA59+khffVV2cIDvK/w5bcJfAJ8wbdo03Xbb\nbbrhhhvsLgU15LPPPlOfPn00duxYRURE6Oqrr9b8+fPtLqvK3BYefvrpJ+Xk5Ojll1/WiBEj9OWX\nX+r222/XHXfcoXXr1rnrsPCAl156SVdccYUeeughu0uBG50/f15PP/207r77bjVs2NDucvCzr782\nVxwyM81y//7mioOXXv1GNVmWpUcffVQDBw5Ut27d7C4H1ZSUlKSUlBS9+OKLdpeCGnTgwAG99dZb\n6ty5s/7+97/rgQce0PTp0/WnP/3J7tKqpMbCw4cffqiQkBCFhISoUaNG2r17tyRp9OjRmj59umJi\nYvTUU09p5MiRmjt3bk0dFm5W+ntdu3atXn/9df3f//2f3aWhmkp/t+vXry96Ly8vT3fddZccDof+\n+Mc/2lglivvsM2nECCk31yzfcIO54uDqhSF6W/I9Dz74oHbs2KGkpCS7S0E1HTlyRI8++qg++OAD\n1a1b1+5yUIMKCgoUGxur5557Tj179tTkyZM1efJkrz0frrFB4kaNGqW4uLii5WbNmikwMPCS21q6\ndu1a4iQFtVvp7/Xjjz/WiRMn1KpVq6J1+fn5evzxx/Xaa6/pwIEDdpSJKij93RY++F4YHA4fPqyv\nv/6aqw61xIcfShMmSPn5Zvm226SPP5Yq0/9EUlISzzz4kIceekh/+9vftG7dOkVFRdldDqpp69at\nOnHihK6++moVPo6an5+vtWvX6o033tD58+flcDhsrhJVERUVVeb58OLFi22qqHpqLDwEBwerXbt2\nJdb17du36ApEoT179ujKK6+sqcPCzUp/r1OmTFF8fHyJbYYOHaoJEybonnvu8XR5qIayfmYLg8OB\nAwe0atUqr+0Jwte8/bY0dapU2L3F3XdL770n8ctJ//XQQw/pr3/9q9asWaPWrVvbXQ5qwE033aTU\n1NQS6yZNmqSuXbvq6aefJjh4sQEDBlxyPrx7926vPR+usfBQlieffFIJCQkaNGiQhgwZos8//1zL\nly/3mafN/VFYWNglJ5R169ZVZGSkOnbsaFNVqAl5eXm68847lZKSouXLl+vixYtK/7kP0CZNmnAZ\n3Sb/8z/Sk086l6dMkd58U6pTx76aYK8HH3xQixYt0rJlyxQcHFz0cxoaGkpX6F4sODj4kudWgoOD\n1bRpUzon8XKPPfaYBgwYoBdffFFjx47Vpk2bNH/+fL3zzjt2l1Ylbh3nYfTo0Zo7d65eeeUVxcTE\naMGCBVq8eLGuueYadx4WHsZvQ3zD0aNHtXz5ch05ckS9evVSixYtFBUVpRYtWmjjxo12l+d3LEua\nObNkcHjySemttwgO/m7u3LnKzs7W9ddfrxYtWhRNH3/8sd2loYbx/6tv6NOnj5YsWaJFixapR48e\nev755zVnzhwlJCTYXVqVuHWcBwBA5eXnS488Yq4wFPrd76T/+A+pKucSjPMAAKgpbr1tCQBQObm5\n5pmGZcuc615/XXr44ervOyEhQYGBgUpMTFRiYmL1dwgA8DtceQCAWiI93fSitHmzWQ4MlObPlyZO\nrN5+ufIAAKgpXHkAgFpg1y4zhsMPP5jlRo2kTz81A8IBAFBbEB4AwGZr10qjR0sZGWa5ZUvpb3+T\nevSwty4AAEpza29LAICKJSVJN9/sDA49e0r/+AfBAQBQOxEeAMAGliW9/LKUmChduGDWDRtmrkL8\nPNg3AAC1DuEBADzswgXp/vulp5+WpGcltVCdOkHKy7tZP/20r8LPLly4UAEBAapTp44CAgIUEBCg\noKAgl46bkJCg+Ph4LVq0qNptAAD4J555AAAP+ukn6c47pW++kaSXJb2h8ePf14wZbTRz5n9p2LBh\n2rlzp6644opy9xEaGqo9e/aosLM8VweSSkpKorclAEC1EB4AwEP++U9pzBjp8OHCNXM0fvxM/elP\nIyVJ77//viIiIrR06VKNHTu23P04HA6Fh4e7v2AAAErhtiUAcDPLkt54Qxo40Bkcmjf/QQ7HcT35\n5I1F2zVq1Ej9+/fXxo0bK9xfTk6O2rRpo9atW2v06NHasWOHO8sHAKAI4QEA3Oj0aSkhwYwQffGi\nWXfNNdL8+cflcDgUERFRYvuIiAgdP3683P117txZCxYs0LJly/TBBx+ooKBA1157rdLS0tzZDAAA\nJBEeAMBtUlOlPn2kjz+WpA8lhahu3RB9910jhYZerNI+4+LiNH78eMXExGjQoEFavHixwsPDNW/e\nvJosHQCmVCkEAAANTElEQVSAMvHMAwC4wXvvSQ8+KJ09a5ZDQkbp5ZfjNGyYWT537pwsy1J6enqJ\nqw/p6enq3bu3y8cJDAxU7969tW9fxb00SVLHjh3lcDgUHR2t6J/7g01MTFRiYqLLxwMA+DfCAwDU\noLNnpYcekhYscK7r3Vv6y1+C1b59uxLbRkZGKjk5WTExMZKk7Oxsbdq0SdOmTXP5eAUFBUpNTdWt\nt9562W337t1Lb0sAgGohPABADfn+e+nuu6Xt253r7r9fmjNHql//0u0fffRR/e53v1OHDh3Upk0b\nzZw5Uy1bttSoUaOKtpk4caKio6P1wgsvSJKee+45xcXFqUOHDsrMzNQrr7yiQ4cO6b777nN38wAA\nIDwAQHUVFJjelGbMkM6fN+uCgqR586Tx48v/3IwZM3TmzBlNmTJFmZmZGjRokD7//PMSYzwcPnxY\nderUKVrOyMjQ/fffr+PHjyssLEyxsbHauHGjunTp4q7mAQBQxGEVjjIEAKi0Q4ek++6TvvzSua57\nd+mjj8y8NsjOzlZoaKiysrK4bQkAUC30tgQAVWBZ0rvvSlddVTI4PPKItHlz7QkOAADUJG5bAoBK\n+vFH6YEHpC++cK6LjjYPSQ8daltZl5WQkKDAwEB6WAIAVBm3LQGAiy5elH7/e+k3v3F2wSpJkyZJ\ns2dLjRvbVlqFuG0JAFBTuPIAAC5Yv16aOlX67jvnuhYtpLffllzoJRUAAJ/AMw8AUIFTp0x3qwMH\nOoNDQID08MPSzp0EBwCAf+HKAwCUIT/fjBL9zDPSiRPO9bGx0ty5Up8+tpUGAIBtuPIAAKV89ZV0\n9dWmC9bC4BASYgZ727SJ4AAA8F+EBwD42c6d0siR0s03lxwleswY89706VKx8dq8TkJCguLj47Vo\n0SK7SwEAeCl6WwLg99LSpOefNyNC5+c718fGmt6VBg+2r7aaQG9LAICawjMPAPzWsWPSyy+bZxjO\nn3eub9lSevFF6e67zcPRAADAIDwA8Dvp6SY0vPWWdO6cc31wsPT009Ljj0tBQfbVBwBAbUV4AOA3\nfvpJevVV6c03Sw7y1qCBNG2a9OSTUvPm9tUHAEBtR3gA4PP27JFee01auFA6c8a5vn596cEHpRkz\npIgI++oDAMBbEB4A+CTLklavNg88L19e8r169cxo0U89JUVF2VKeLRISEhQYGKjExEQlJibaXQ4A\nwAvR2xIAn3LhgpSUJM2eLaWklHwvONiM3TBjhtSihT312YHelgAANYUrDwB8Qnq6NH++9MYb0vHj\nJd9r1cqM0XDffVLjxvbUBwCALyA8APBaeXnSF19I775rbk3Kyyv5ft++puekO++U6ta1p0YAAHwJ\n4QGA19m3T1qwQHrvPTNWQ3EBAdLtt0uPPSZde63kcNhSIgAAPonwAMAr5ORIS5aYqwxr1lz6flSU\nNGmSNHmy1Latx8sDAMAvMHYqgFrr7Flp8WJp3Dgz/sKECSWDQ2CgNHq09Nln0qFD0gsv+H5wWLJk\niYYNG6ZmzZopICBA27dvd/mzCQkJio+P16JFi9xYIQDAl3HlAUCtcuGC9NVXpsekpUul06cv3aZz\nZ+nee02Y8LfxGXJzczVo0CCNGzdOkydPrtRnk5KS6G0JAFAthAcAtsvKklauNFcQVqyQMjIu3aZZ\nM2nMGGn8eP9+lmH8+PGSpIMHD4qetgEAnkZ4AGCLvXtND0mffSatW3dpT0mSFBoq3XGHuW3phhvo\nMQkAALsRHgB4RF6etH69CQvLl0u7d5e9XUiINHKklJAgDRtmRoMGAAC1A+EBgFtYlnTggJScbKa/\n/13KzCx723btpNtuM6Fh8GDpiis8W2tt9eGHH2rKlCmSJIfDoc8//1wDBgywuSoAgD8jPACoMceO\nSV9/7QwMhw6VvV1AgDRggAkLt90mdeniv88wVGTUqFGKi4srWo6Ojq7W/hISEhQYWPKf/cTERCUm\nJlZrvwAA/0F4AFAlliX9+KP0zTdmWrdO2rmz/O1DQ6Xhw01YGD5catrUY6V6reDgYLVr167c9x2V\nTFz0tgQAqC7CAwCXXLwopaaa5xYKA0NaWvnb169vri7ceKN52Dk21ozLgOrJyMjQoUOHdPToUVmW\npV27dsmyLEVGRirC3/qtBQB4nMOirz8ApRQUmN6QNm92Tt9+K507V/5nAgOlPn1MWLjxRumaa0yA\nQM1auHCh7rnnnkuuOsyaNUvPPvtsmZ/Jzs5WaGiosrKyuPIAAKgWwgPg5yxLOnKkZFDYssWMvVCR\nhg3NeAsDB5qpXz8pONgzNaNyCA8AgJrCTQSAHzl/XtqxQ9q+Xdq2zTk/efLyn23fXurb11xRGDhQ\nionhNiRvU/jANA9JAwCqiisPgA8qKJAOHzZBITXVGRR27Sp7MLbSoqJMUOjb11xR6NNHatLE/XXD\nPbjyAACoKfzeEPBieXnS/v0mJOzcaaYdO0xIOHPGtX1ERJirCIVhoW9fqZo9ggIAAB9FeABqubw8\ncxVh3z7ntHev8/XFi67tJzBQ6tbNBIWePZ1zOugBAACuIjwAtcDFi9LBg5cGg337pB9+cD0gSGYA\ntnbtpK5dTVjo1s2EhK5dGbkZAABUD+EB8ICLF02PRj/+aEJC4VR8OT+/cvusV0/q0MEZEgrnnTrR\nRSoAAHAPwgNQTfn5Unq6dPSoCQhHj5rp8GFnQEhLMw8xV1aDBiYgFJ86djTz6GhzlQFwFb0tAQCq\ni96WgAqcPXtpKCj9+vjxyl81KC40VGrb1hkKik9RUVKpscCASqO3JQBATeHKA/zOhQvmSkF6ujnx\nL5wXf104z86u/vHCw6UrrzRTmzbO14VT48bVPwYAAIAnEB7g9c6dk/79bzPQWXlT8VBw6lTNHTsi\nwtw+1LKlmZd+3bo1oy4DAADfQXhArXL+vJSRUXEQKJwKA0NOTs3X0aiRCQYVhYOoKHovAgAA/oXw\ngBplWeZkPjPThICMjMq9PnvWfbUFBUmRkWaKiCg5L72uQQP31QEAAOCtCA8okp8vnT5t7vOvaCq+\nTekAkJlpBjVzt4AAqVkz16amTaXmzaWGDd1fF1Cb0dsSAKC66G3JixUUSLm5zikn59J5Ts7lw0Bh\nIMjNtacdwcFSWJh5cDgszEyXCwShoXRTCriK3pYAADWFKw9uVlBgHug9e1Y6c8ZMpU/yyzvxv9zc\nnbf4VIbD4TzxLx4AXHkdGspzAwAAAN7CL8NDQYHzZL74vKx1VX2v8PW5c3a3tnwBAebB4NJTSEjZ\n6yuauAoAAADg+zweHgoKTI86584559V5XdnPnTlj+vn3RkFB5hafhg1dnzdsWP4Jf1AQA5ABAADA\ndW4LDykp0l13XXoCf/Giu45ov/r1TS89QUFmXvx18XllTv4L50FB/HYfAAAA9nJbeCgokPbtc9fe\nXVO/vpnq1XPOyzqZL+9EvzLv16/PyT2AylmyZInmzp2rrVu36tSpU0pJSVFMTEyFn1m4cKHuuece\nORwOFfZ3Ub9+fZ05c+ayx6O3JQBAdbktPAQFSU2aXHoC74nX9etLdetySw6A2i03N1eDBg3SuHHj\nNHnyZJc/Fxoaqj179hSFB4eL/9glJSXR2xIAoFrcFh66dDEjAAMAyjZ+/HhJ0sGDB1WZXrMdDofC\nw8PdVRYAAOXiRhsA8DI5OTlq06aNWrdurdGjR2vHjh12lwQA8BOEBwDwIp07d9aCBQu0bNkyffDB\nByooKNC1116rtLQ0u0sDAPgBwgMAeMCHH36okJAQhYSEqFGjRlq/fn2V9hMXF6fx48crJiZGgwYN\n0uLFixUeHq558+bVcMUAAFzKLweJAwBPGzVqlOLi4oqWo6Oja2S/gYGB6t27t/a50L1dYW9LxdHz\nEgCgMggPAOABwcHBateuXbnvu9pjUmkFBQVKTU3Vrbfeetlt6W0JAFBdhAcAsElGRoYOHTqko0eP\nyrIs7dq1S5ZlKTIyUhEREZKkiRMnKjo6Wi+88IIk6bnnnlNcXJw6dOigzMxMvfLKKzp06JDuu+8+\nO5sCAPATbg8Px46ZqTz160vdulW8jx07zOjU5YmKMlN5zp6Vdu6s+Bhdu5rB3spDO5xoh0E7nGiH\nU2XasWzZsqIB3xwOR9HtQ5Mnz9L99z/78/4OKzOzjv71L/OZ3bsz9O679ys9/bjCwsIUGxurjRs3\nqkuXLuW2IyfHzFNSzIj1fB9OtMOJdhi0w4l2OHmiHV7DcrNZsyxLKn/q1u3y++jWreJ9zJpV8ee/\n+67iz0tmG9pBO2gH7fDNdmRZkn6ee3M7fOX7oB20g3bQDu/lsCzLcmc4IVE60Q6DdjjRDifaYbij\nHTk52bruulCtWZOlhg0beW07SqMdTrTDiXYYtMPJW9rhLdweHgAA9srOzlZoaKhuueUWBQYG0sMS\nAKDKCA8A4OMKw0NWVha9LQEAqoVB4gAAAAC4hCsPAODjLMvS6dOnFRISUuXxJAAAkAgPAAAAAFzE\nbUsAAAAAXEJ4AAAAAOASwgMAAAAAlxAeAAAAALiE8AAAAADAJYQHAAAAAC4hPAAAAABwyf8D1jeZ\nm1ewCykAAAAASUVORK5CYII=\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": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "graph.save('glo_atan.pdf', aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (U, V, th, ph))" ] }, "execution_count": 16, "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": 17, "metadata": { "collapsed": false }, "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": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XNC.coord_range()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "U = arctan(u)\n", "V = arctan(v)\n", "th = th\n", "ph = ph" ] }, "execution_count": 18, "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": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "u = tan(U)\n", "v = tan(V)\n", "th = th\n", "ph = ph" ] }, "execution_count": 19, "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": 20, "metadata": { "collapsed": false, "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*sin(th)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V)*sin(th)^2 + cos(U)^2*sin(V)^2*sin(th)^2)/(cos(U)^2*cos(V)^2) dph*dph" ] }, "execution_count": 20, "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": 21, "metadata": { "collapsed": false }, "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": 21, "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": 22, "metadata": { "collapsed": false }, "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": 22, "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": 23, "metadata": { "collapsed": false }, "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*sin(th)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V)*sin(th)^2 + cos(U)^2*sin(V)^2*sin(th)^2) dph*dph" ] }, "execution_count": 23, "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": 24, "metadata": { "collapsed": false }, "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": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g22 = gt[XNC.frame(), 2, 2, XNC].expr()\n", "g22" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sin(-U + V)^2" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g22.factor().reduce_trig()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(cos(V)^2*sin(U)^2*sin(th)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V)*sin(th)^2 + cos(U)^2*sin(V)^2*sin(th)^2)/sin(th)^2" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g33st = gt[XNC.frame(), 3, 3, XNC].expr() / sin(th)^2\n", "g33st" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sin(-U + V)^2" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g33st.factor().reduce_trig()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "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": 29, "metadata": { "collapsed": false }, "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": 29, "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": 30, "metadata": { "collapsed": false }, "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": 30, "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": 31, "metadata": { "collapsed": false }, "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": 31, "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": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (tau, ch, th, ph))" ] }, "execution_count": 32, "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": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "tau: (-pi, pi); ch: (0, pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC.coord_range()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "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": 34, "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": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "tau = U + V\n", "ch = -U + V\n", "th = th\n", "ph = ph" ] }, "execution_count": 35, "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": 36, "metadata": { "collapsed": false }, "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": 36, "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": 37, "metadata": { "collapsed": false }, "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": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(Omega^2).display()" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "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": 38, "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": 39, "metadata": { "collapsed": false, "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": 39, "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": 40, "metadata": { "collapsed": false }, "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": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tc = XC_to_XS(tau,ch,th,ph)[0]\n", "tc" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sin(tau)/(cos(ch) + cos(tau))" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tc.reduce_trig()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "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": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rc = XC_to_XS(tau,ch,th,ph)[1]\n", "rc" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sin(ch)/(cos(ch) + cos(tau))" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rc.reduce_trig()" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " t == t\n", " r == r\n", " th == th\n", " ph == ph\n", " tau == arctan((sin(ch) + sin(tau))/(cos(ch) + cos(tau))) + arctan(-(sin(ch) - sin(tau))/(cos(ch) + cos(tau)))\n", " ch == arctan((sin(ch) + sin(tau))/(cos(ch) + cos(tau))) - arctan(-(sin(ch) - sin(tau))/(cos(ch) + cos(tau)))\n", " th == th\n", " ph == ph\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": 45, "metadata": { "collapsed": false }, "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": 45, "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": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUUAAAJHCAYAAAAHVETLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nqkSGoiRJUiUyFCVJkir5f0dn/1lO1XYuAAAAAElFTkSuQmCC\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, nb_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": 47, "metadata": { "collapsed": true }, "outputs": [], "source": [ "graph.save('glo_conf_diag_Mink.pdf')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some blow-up near $i^0$:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWYAAAJFCAYAAADu9l0TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEFIAAAAASUVORK5CYII=\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, nb_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": {}, "source": [ "To produce a more satisfactory figure, let us use some logarithmic radial coordinate:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (t, rh, th, ph))" ] }, "execution_count": 49, "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": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t = t\n", "rh = log(r)\n", "th = th\n", "ph = ph" ] }, "execution_count": 50, "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": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t = t\n", "r = e^rh\n", "th = th\n", "ph = ph" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XL.inverse().display()" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": 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": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWYAAAJFCAYAAADu9l0TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\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)}, nb_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": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUUAAAJHCAYAAAAHVETLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\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", " nb_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": 55, "metadata": { "collapsed": true }, "outputs": [], "source": [ "graph.save('glo_conf_Mink_null.pdf')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conformal factor\n", "\n", "The conformal factor expressed in various coordinate systems:" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "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": 56, "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": 57, "metadata": { "collapsed": false }, "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": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.expr(XC)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 58, "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": 59, "metadata": { "collapsed": false }, "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": 59, "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": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "