{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Geodesics in anti-de Sitter spacetime\n", "\n", "This worksheet aims at recovering some geodesics of anti-de Sitter (AdS) spacetime using numerical tools implemented in the SageMath class **IntegratedGeodesic**." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "*NB:* a version of SageMath at least equal to 8.1 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 8.1.beta2, Release Date: 2017-08-13'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "First set up the notebook to display mathematical objects using LaTeX rendering:" ] }, { "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": [ "## Anti-de Sitter manifold\n", "\n", "To set AdS spacetime, declare a 4-dimensional differentiable manifold and a non-negative parameter $b$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "AdS = Manifold(4, 'AdS', r'\\mathcal{Schw}')\n", "b = var('b') ; assume(b > 0)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Define the hyperbolic coordinates:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Hyp. = AdS.chart(r'ta:\\tau rh:(0,+oo):\\rho th:(0,pi):\\theta ph:(0,2*pi):\\phi')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Finally set the Lorentzian metric of Ads spacetime:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = -cosh(rh)^2 dta*dta + b^(-2) drh*drh + sinh(rh)^2/b^2 dth*dth + sin(th)^2*sinh(rh)^2/b^2 dph*dph" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = AdS.lorentzian_metric('g')\n", "g[0,0], g[1,1] = -cosh(rh)^2, b^(-2)\n", "g[2,2], g[3,3] = b^(-2)*sinh(rh)^2, b^(-2)*sinh(rh)^2*sin(th)^2\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "deletable": true, "editable": true }, "source": [ "## Geodesics of AdS spacetime" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Defining an affinely parametrised geodesic" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Declare the various variables needed to define a geodesic; start with the affine parameter and its extremal values:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "affine_param = var('s s_0 s_max')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Then, declare the starting point of the geodesic:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "initial_pt_coords = var('ta_0 rh_0 th_0 ph_0')\n", "p_0 = AdS.point(initial_pt_coords, name='p_0')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Declare the initial tangent vector:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "initial_tgt_vec_comps = var('Dta_0 Drh_0 Dth_0 Dph_0')\n", "v_0 = AdS.tangent_space(p_0)(initial_tgt_vec_comps)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The parametrised geodesic may now be initialised:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The curve was correctly set.\n", "Parameters appearing in the differential system defining the curve are [Dph_0, Drh_0, Dta_0, Dth_0, b, ph_0, rh_0, s_0, s_max, ta_0, th_0].\n" ] } ], "source": [ "geod = AdS.integrated_geodesic(g, affine_param, v_0, verbose=True)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the system of the affinely parametrised geodesic equations:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Geodesic in the 4-dimensional differentiable manifold AdS equipped with Lorentzian metric g on the 4-dimensional differentiable manifold AdS, and integrated over the Real interval (s_0, s_max) as a solution to the following geodesic equations, written with respect to Chart (AdS, (ta, rh, th, ph)):\n", "\n", "Initial point: Point p_0 on the 4-dimensional differentiable manifold AdS with coordinates [ta_0, rh_0, th_0, ph_0] with respect to Chart (AdS, (ta, rh, th, ph))\n", "Initial tangent vector: Tangent vector at Point p_0 on the 4-dimensional differentiable manifold AdS with components [Dta_0, Drh_0, Dth_0, Dph_0] with respect to Chart (AdS, (ta, rh, th, ph))\n", "\n", "d(ta)/ds = Dta\n", "d(rh)/ds = Drh\n", "d(th)/ds = Dth\n", "d(ph)/ds = Dph\n", "d(Dta)/ds = -2*Drh*Dta*sinh(rh)/cosh(rh)\n", "d(Drh)/ds = -Dph^2*cos(th)^2*cosh(rh)*sinh(rh) - (Dta^2*b^2 - Dph^2 - Dth^2)*cosh(rh)*sinh(rh)\n", "d(Dth)/ds = (Dph^2*cos(th)*sin(th)*sinh(rh) - 2*Drh*Dth*cosh(rh))/sinh(rh)\n", "d(Dph)/ds = -2*(Dph*Drh*cosh(rh)*sin(th) + Dph*Dth*cos(th)*sinh(rh))/(sin(th)*sinh(rh))\n", "\n" ] } ], "source": [ "sys = geod.system(verbose=True)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Computing and plotting the geodesic\n", "\n", "#### Null radial geodesic\n", "\n", "Set a dictionnary providing numerical values for each of the parameters apprearing in the system defining the geodesic. \n", "\n", "The values suggested below make the initial tangent vector null and radial." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "params_values_null_radial = {b:1, s_0:0, s_max:15, ta_0:0, rh_0:0.1, th_0:pi/3, ph_0:pi/4, \n", " Dta_0:1/cosh(0.1), Drh_0:1, Dth_0:0, Dph_0:0}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Then integrate the geodesic for such values of the parameters:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing 4th order Runge-Kutta integration with Maxima by default...\n", "Numerical integration completed.\n", "\n", "Checking all points are in the chart domain...\n", "All points are in the chart domain.\n", "\n", "The resulting list of points was associated with the key 'null_radial' (if this key already referred to a former numerical solution, such a solution was erased).\n" ] } ], "source": [ "sol_null_radial = geod.solve(step=0.1, parameters_values=params_values_null_radial, \n", " solution_key='null_radial', verbose=True)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Analytic expressions of null geodesics in AdS being known, these may be used to check the previous numerical solution:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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fX1AqlcKtW7eKpl2+fFmQy+XF9p8glNxPldn2+o7rssbJ+PHjBUdHR+Hhw4fF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\n5RM5YxJNJwEAACAI8TkNAezV1a9q0/5NWvXnVQwGAAAAlBl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Kj4+XJC1btkxPPPGEpk6dqoMHDyohIUFpaWnq1q1bk20eO3ZMM2bMUGFhoSIjI5WSkqK3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\n8YILrK0DAAAAaG2EBg9t2SK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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rh_num = []\n", "rh_analyt = []\n", "rh_error = []\n", "\n", "for (S,TA,RH,TH,PH) in sol_null_radial:\n", " rh_num += [(S,RH)]\n", " rh_analyt += [(S, arcsinh(S + sinh(0.1)))]\n", " rh_error += [(S, RH - arcsinh(S + sinh(0.1)))]\n", "\n", "plot_rh_num = line(rh_num, legend_label=r'Numerical solution for coordinate $\\rho$', color='green')\n", "plot_rh_analyt = line(rh_analyt, color='orange', legend_label=r'Analytical solution for coordinate $\\rho$', \n", " linestyle='--')\n", "plot_rh_error = line(rh_error)\n", "\n", "(plot_rh_num + plot_rh_analyt).show()\n", "plot_rh_error.show(title=r'Error on coordinate $\\rho$')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The following results provide another way to check the numerical integration.\n", "\n", "The squared norm $g_{\\mu\\nu} \\dot{x}^{\\mu} \\dot{x}^{\\nu}$ of the vector tangent to any geodesic with respect to any affine parameter $s$ is constant throughout motion.\n", "\n", "In addition, $\\partial_{\\tau}$ is an obvious Killing vector of AdS metric, so that quantity $e \\equiv \\cosh^{2}(\\rho) \\ \\dot{\\tau}$ is constant as well.\n", "\n", "Therefore, using an interpolation of the previous numerical solution, one may check that these two quantities are conserved (not to be disturbed by initial edge effects, the reference values used to check conservations of the various quantities are updated after 10 steps):" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing cubic spline interpolation by default...\n", "Interpolation completed and associated with the key 'null_radial' (if this key already referred to a former interpolation, such an interpolation was erased).\n" ] }, { "data": { "image/png": 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UBqGhEiE0AAAAwBfl3XcMudBApQEAAAChjuFJfrJqaAAAAAC8RWiopKg0AAAA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\nVYSJ0IQGAAAAoAKrCHeEJjQAAAAAFRi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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interp_null_radial = geod.interpolate(solution_key='null_radial', interpolation_key='null_radial', verbose=True)\n", "\n", "error_squar_norm_null_radial = []\n", "error_e_null_radial = []\n", "\n", "i = 0\n", "for (S,TA,RH,TH,PH) in sol_null_radial:\n", " P = geod(S, interpolation_key='null_radial')\n", " V = geod.tangent_vector_eval_at(S, interpolation_key='null_radial')\n", "\n", " squar_norm_null_radial = numerical_approx((g.at(P)(V,V)).substitute({b:1}))\n", " e_null_radial = numerical_approx((-g.at(P)[0,0]*V[0]).substitute({b:1}))\n", " \n", " if i == 0:\n", " squar_norm_null_radial_0 = squar_norm_null_radial\n", " e_null_radial_0 = e_null_radial\n", " \n", " if i == 10:\n", " squar_norm_null_radial_0 = squar_norm_null_radial\n", " e_null_radial_0 = e_null_radial\n", "\n", " error_squar_norm_null_radial += [(S,squar_norm_null_radial - squar_norm_null_radial_0)]\n", " error_e_null_radial += [(S,e_null_radial - e_null_radial_0)]\n", " \n", " i += 1\n", "\n", "plot_error_squar_norm_null_radial = line(error_squar_norm_null_radial)\n", "plot_error_e_null_radial = line(error_e_null_radial)\n", "\n", "plot_error_squar_norm_null_radial.show(title=\"Null, radial geodesic: error on conservation of squared norm\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_e_null_radial.show(title=\"Null, radial geodesic: error on conservation of e\", \n", " ymin=-1e-3, ymax=1e-3)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "One may finally plot the time coordinate of the geodesic with respect to radial coordinate:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "data": { "image/png": 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hq4bo04Of6qm6T2lC6wnK6ZPTdCwAADIM5QEAMkD01Wh1WdBFkTGRmtVplvrU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\na3qtoTgAAAC4EcoDstSOUzs0cfdEvdP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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "geod.plot_integrated(interpolation_key='null_radial', ambient_coords=(rh,ta), plot_points=200, color='green')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "deletable": true, "editable": true }, "source": [ "#### Timelike radial geodesic\n", "\n", "Set a dictionnary providing numerical values for each of the parameters apprearing in the system defining the geodesic. \n", "\n", "The values suggested below make the initial tangent vector timelike and radial, with squared norm equal to -1, so that the curve parameter `s` is proper time along the (timelike) geodesic." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "params_values_timelike_radial = {b:1, s_0:0, s_max:3, ta_0:0, rh_0:0.1, th_0:pi/3, ph_0:pi/4, \n", " Dta_0:sqrt(2)/cosh(0.1), Drh_0:1, Dth_0:0, Dph_0:0}" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Integrate the geodesic for such values of the parameters:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing 4th order Runge-Kutta integration with Maxima by default...\n", "Numerical integration completed.\n", "\n", "Checking all points are in the chart domain...\n", "All points are in the chart domain.\n", "\n", "The resulting list of points was associated with the key 'timelike_radial' (if this key already referred to a former numerical solution, such a solution was erased).\n" ] } ], "source": [ "sol_timelike_radial = geod.solve(step=0.01, parameters_values=params_values_timelike_radial, \n", " solution_key='timelike_radial', verbose=True)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Use the analytic solution to check the numerical integration:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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g0hPFJVnQxA3ELSjRadBRDgxEZHJszG2w/YXtUKlVeHHbi9BJOtFJRPQXDg1E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uZxokSZKUPw4cgPbtoXJl+Mc/gk6jguLuSZIkSTpqvXvDggXw/vtQtmzQaVRQ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\nBmnRokVas2aN6tate8bnWrRoob179yo8PPycz51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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rh_num = []\n", "rh_analyt = []\n", "rh_error = []\n", "\n", "for (S,TA,RH,TH,PH) in sol_timelike_radial:\n", " rh_num += [(S,RH)]\n", " rh_analyt += [(S, arcsinh(sinh(0.1)*cos(S) + cosh(0.1)*sin(S)))]\n", " rh_error += [(S, RH - arcsinh(sinh(0.1)*cos(S) + cosh(0.1)*sin(S)))]\n", "\n", "plot_rh_num = line(rh_num, legend_label=r'Numerical solution for coordinate $\\rho$', color='green')\n", "plot_rh_analyt = line(rh_analyt, color='orange', legend_label=r'Analytical solution for coordinate $\\rho$', \n", " linestyle='--')\n", "plot_rh_error = line(rh_error)\n", "\n", "(plot_rh_num + plot_rh_analyt).show()\n", "plot_rh_error.show(title=r'Error on coordinate $\\rho$')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Interpolate the solution to check conservation of norm and quantity $e$, and plot the solution:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing cubic spline interpolation by default...\n", "Interpolation completed and associated with the key 'timelike_radial' (if this key already referred to a former interpolation, such an interpolation was erased).\n" ] }, { "data": { "image/png": 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4J6ih4ciRI4qMjNTXX38tj8f/TKgqVapIkjZs2OBbFhcX57dO/fr1JUktW7bU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\nAM5yXWgI1kgDsycBAAAgXBE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kSZLy0957w733QmUlvPJKeN71r3/1KtMusDxIkiQpvw0dCrNnwymnwHnnwaBB\n8OGHsVPlJMuDJEmS8t9ee8Edd8DkyaFI9OgBr70WO1XOKY4dQJIkScqYwYNDebj11nCNSTXia0uS\nJEmS0uK1JUmSJElpsTxIkiRJSovlQZIkSfqqdevghRdip8hKlgdJkiTpq269Ffr1g5tucifEFnxt\nSZIkSfqqiy+GBQtg1Ch4+WX4y1+gUaPYqbKCJw+SJEnSVxUXw/XXw/jx8Mgj8PWvwyefxE6VFSwP\nkiRJ0taccQY8/zwsXQp9+8Kbb8ZOFJ3lQZIkSdqWnj1DgSgpgSOPhJkzYyeKyvIgSZIkbc+++8KM\nGXD88dCqVew0UWX1hunBgwdTXFxMMpkkmUzGjiVJkiQVtKwuD1VVVTRt2jR2HEmSJEl4bUmSJElS\nmiwPkiRJktJieZAkSZJ21fr1sRNkhOVBkiRJ2hUvvgidOsHrr8dOUucsD5IkSdKu6N4d9t4bhgzJ\n+03UlgdJkiRpVzRpAo8+CtXVUFaW11eYLA+SJEnSrtp3X6isDFeXfvzj2GnqjOVBkiRJqg2HHgrX\nXQc33xxOIvKQS+IkSZKk2pJKhatLL7wAr74KbdrETlSranzyMGPGDMrKyigtLaWoqIjKysrtfn76\n9OkUFRX921e9evVYvHjxToeWJEmSslIiAXfcAQ0awIQJsdPUuuKa/oTVq1dzyCGHcO6553Lqqaem\n9XMSiQRz586lSZMmX/xYy5Yta/qtJUmSpOzXvDnMng177hk7Sa2rcXkYNGgQgwYNAqAmN55atGjh\nFSRJkiQVhjwsDpChgelUKsUhhxxCmzZtGDhwIDNnzszEt5UkSZJUi+q8PLRu3Zo//elPPPDAAzz4\n4IO0bduWY445hlmzZtX1t5YkSZJUi2p8bammDjjgAA444IAv/rpPnz6888473HTTTYwdO7auv70k\nSZKkWlLn5WFrjjjiCJ577rkdfq5z584kEglKS0spLS0FIJlMkkwm6zqiJEmSpC1EKQ+zZs2idevW\nO/zcvHnzHLKWJEmSssROPdX69ttvf/HS0rvvvsurr75Ks2bNaNu2LT/5yU/45JNPvriSdPPNN9Oh\nQwcOPPBA1q1bx5///GeeeuopHn/88dr9lUiSJEnZ6oYb4N134dZbYyfZJTUuD//4xz/o378/iUSC\nRCLBZZddBsCIESMYM2YMCxcuZP78+V98fsOGDVx22WV88sknNGrUiJ49ezJt2jSOOuqo2vtVSJIk\nSdmsujo7RzyVAAAgAElEQVQsj7vhBmjUKHaanZZI1WRZQ4asWLGCkpISqqqqvLYkSZKk3DdnDhx4\nIEyZAscfHzvNTsvIngdJkiSpoHXrBm3awJNPxk6ySywPkiRJUl1LJKB3b3j55dhJdonlQZIkScqE\nXr3gtddip9gllgdJkiQpE/bfHz79FFasiJ1kp1keJEmSpEz4v6XHLFoUN8cusDxIkiRJmdClC/zu\nd7DXXrGT7DSfapUkSZKUFk8eJEmSJKXF8iBJkiQpLZYHSZIkSWmxPEiSJElKi+VBkiRJUlqyujyU\nl5dTVlZGRUVF7CiSJElSwfOpVkmSJKmuffwxzJgBJ50Eu+8eO81Oy+qTB0mSJCkvPPggDB8OmzbF\nTrJLLA+SJElSXauogAEDoEmT2El2SXHsAJIkSVJemzsXnn8e7rkndpJd5smDJEmSVJduuQWaN4dh\nw2In2WWWB0mSJKmufPYZjBkDF1wADRvGTrPLLA+SJElSXbnxRqiuhksuiZ2kVlgeJEmSpLrw0Udw\n001w0UXQsmXsNLXCgWlJkiSpLrRqBddeG55ozRMuiZMkSZKUFq8tSZIkSUqL5UGSJElSWiwPkiRJ\nktJieZAkSZKUFsuDJEmStKuqqsJXnvOpVkmSJGlXbNgAp54KmzbBU09BIhE7UZ3J6vJQXl5OcXEx\nyWSSZDIZO44kSZL071IpOO88mDEDHn88r4sDuOdBkiRJ2nk/+xlcdRVUVEB5eew0dc6ZB0mSJGln\n/PrXoThcd11BFAewPEiSJEk1d+WV8POfwy9/CT/8Yew0GZPVMw+SJElS1rn1VvjFL+Dqq+EnP4md\nJqMsD5IkSVJNnHYa7LYbfPvbsZNknAPTkiRJktLizIMkSZKktFgeJEmSJKXF8iBJkiQpLZYHSZIk\n6atSKfjDH+COO2InyTqWB0mSJOlzq1fD2WfDxRfD3Lmx02Qdn2qVJEmSAN55B4YNC3+sqCiYrdE1\n4cmDJEmSNG4cHHoorFsHL75ocdgGy4MkSZIKV1VVuKZ09tkwdCi8/DL06BE7Vdby2pIkSZIK1z/+\nAY8+CnffDWedFTtN1rM8SJIkqXAddxy8/z7suWfsJDkhq68tlZeXU1ZWRkVFRewokiRJylcWh7Ql\nUqlUKnaILa1YsYKSkhKqqqpo2rRp7DiSJEmSyPKTB0mSJGmXLVsWO0HesDxIkiQpP61aBZdfDh07\nwkcfxU6TFxyYliRJUn5JpeChh+DSS2HJEvjFL2CffWKnyguePEiSJCl/vPMODBkCp54KPXvCnDnw\n4x9Dsb9nXhssD5IkScp969bBlVfCgQfC7Nnw8MMwcSJ06BA7WV6xPEiSJCn3zZwJV10Fo0aF04aT\nToJEInaqvOP5jSRJknLfscfCe+9BaWnsJHnNkwdJkiTlB4tDnbM8SJIkSUqL5UGSJEnZrboaxo+H\nu++OnaTgWR4kSZKUnVIpmDoVDj8ckkl4/PHYiQqe5UGSJEnZ58UX4bjjYNAgaNQIZsyAsWNjpyp4\nlgdJkiRlj//937DgrU8fWLwYKitDcejXL3Yy4VOtkiRJyhapFAwbBmvXhlOGs86CevVip9JXWB4k\nSZKUHRKJsBm6fXvYbbfYabQViVQqlYodYksrVqygpKSEwYMHU1xcTDKZJJlMxo4lSZIkFbSsLg9V\nVVU0bdo0dhxJkiTVls2bvYqUwxyYliRJUt17/30YORL69g17G5STLA+SJEmqO//7vzBiBHTqBPfd\nFwaiN22KnUo7yYFpSZIk1b5XXoGrroIHH4Q2beCGG+D886Fx49jJtAssD5IkSapdZ58N48ZBx47w\npz/B8OG+npQnLA+SJEmqXUcdBSecAKefDsX+z8184mtLkiRJktLiwLQkSZKktFgeJEmSlJ758+Gy\ny+DMM2MnUSSWB0mSJG3fK6/AOeeEAei//hXat3dXQ4HKSHmYMWMGZWVllJaWUlRURGVlZSa+rSRJ\nknbW5s3w0ENw9NFw6KHwzDNw/fXh9OHqq6HI34MuRBn5d3316tUccsgh3HLLLSQSiUx8S0mSJO2s\nDRuge3c45ZRQIu67D955By69FJo0iZ1OEWXk7axBgwYxaNAgALLwcSdJkiR9VYMGoSgcfjh87Wux\n0yiL+PCuJEmS/tN3vxs7gbKQl9UkSZIKzYoVsGRJ7BTKQZYHSZKkQvHGGzByJJSWwq9+FTuNclBW\nX1vq3LkziUSC0tJSSktLAUgmkySTycjJJEmScsTGjeHVpFtuCS8m7bMPjBoFF1wQO5lyUFaXh3nz\n5tG0adPYMSRJknLPokVw221w++2wYAEcdRSMHw/DhoWBaGknZKQ8rF69mrfffvuLl5beffddXn31\nVZo1a0bbtm0zEUGSJKmwfPAB3HBDWO42ciQcdFDsRMoDiVQG3k6dPn06/fv3/48dDyNGjGDMmDH/\n8fkVK1ZQUlJCVVWVJw+SJEk7a+VK9zKoVmWkPNSU5UGSJEnKPr62JEmSlEtWrIDRo+HrX4fly2On\nUYGxPEiSJGW7VAqefx7OPRdat4bvfQ/23huWLYudTAUmq19bkiRJKmiffQZ33w1//nPY0bDffvCT\nn8C3vhV2NUgZZnmQJEnKVqefDtOnw0knhZeTBgyAIi+OKB7LgyRJUrb63e+gRQto1Sp2EgmwPEiS\nJGWvHj1iJ5D+jeVBkiQp0957D+68M8wtXHBB7DRS2rw0J0mSlAmrV8Pf/gb9+0PHjnDTTbBgQexU\nUo148iBJklRXUimYORPuuAMmTAgbn/v3DyXilFOgcePYCaUasTxIkiTVlcceg0GDwhOro0bBiBHQ\noUPsVNJOszxIkiTVlWOPhSefhKOP9olV5QXLgyRJUl2pXz9cU5LyRFZX4PLycsrKyqioqIgdRZIk\n6UsLFsBvfxtOFjZujJ1GypisPnkYP348TZs2jR1DkiQpvJb08MNw113w+ONQXBw2Py9bBi1bxk4n\nZURWlwdJkqSoUqkws/C3v8GDD8KqVdCvH4weDaedBnvuGTuhlFGJVCqVih1iSytWrKCkpISqqipP\nHiRJUjypFHTpEv78nHPg7LN9LUkFzZMHSZKkbUkk4JlnoFWr8OdSgcvqgWlJkqQ6tXo1rFu3/c/s\ns4/FQfo/lgdJklRYNm+GadPgm98MxWD8+NiJpJzhtSVJkpT/Uil4/XUYNy58ffwxdOoEP/yhexik\nGrA8SJKk/HbPPXD11TB7NjRrBuXlYfi5d2+vI0k1ZHmQJEn5bcMGOPhguPZaGDAAGjSInUjKWT7V\nKkmSJCktnjxIkqTctH49TJkSrh6VlcVOIxUEX1uSJEm5Y/NmeOopOP/88FLSySeHmQZJGeHJgyRJ\nym6pFLzySigJ48eHl5I6dIDvfQ+SSTjwwNgJpYJheZAkSdlt6lQYPBhatoQzzoAzz/SlJCkSy4Mk\nScpu/fuH2YbjjoNi/6eLFJMzD5IkKa7Vq7f/93fbDY4/3uIgZYGsLg/l5eWUlZVRUVERO4okSapN\nixfDrbfC0UfDAQeEQWhJWc89D5IkKTM++wwefBDuvReefBKKiuAb3wgbn5NJl7dJOcDzP0mSVLeW\nLYOzz4bHHoPqajjmGLjtNjjlFGjePHY6STVgeZAkSXVrzz2hcWO46Sb47/8O+xkk5STLgyRJqluJ\nBEyYEDuFpFqQ1QPTkiQpi61bB488AiNGwKpVsdNIygDLgyRJSt+6dfDww3DWWWFp28knwz//CR9+\nGDuZpAzw2pIkSdqxRx4JryRNnBhOGXr0gMsvh9NOg27dYqeTlCE+1SpJknasb9+wzO2008JX166x\nE0mKwJMHSZK0Y489Bk2axE4hKTJnHiRJKmRr1sD998OCBdv/nMVBEpYHSZIKz+eF4fTToUWLcA1p\n6tTYqSTlAK8tSZJUCFavhsmT4b77YNKkUCB69YKf/SwsbuvcOXZCSTnA8iBJUiH49rfDa0mHHgo/\n/3koDJ06xU4lKcf42pIkSYVgzhzYbTfYf//YSSTlME8eJEnKdVVVsGFDmF/Ylu7dM5dHUt5yYFqS\npFy0dCmMGQNDhoRNz9dfHzuRpAKQ1ScP5eXlFBcXk0wmSSaTseNIkhTXggXw0EPwwAMwfTpUV8N/\n/VcoDsOGxU4nqQA48yBJUi648Ua4/HKoVw/694dTT4WTT4ZWrWInk1RAsvrkQZIk/Z/jjgvXlMrK\noFmz2GkkFShPHiRJii2VCnsXGjeOnUSStsuBaUmSYkil4KWX4P/7/+CAA+DCC2MnkqQd8tqSJEmZ\nsnkzPPccPPhg+Jo/H5o3D7MLPgwiKQdYHiRJyoQpU+Cb34RFi6BNGzjllDD03K8fFPuPY0m5wf+2\nkiQpEzp1gnPOCaWhd28o8uawpNzjwLQkSbUhlYJEInYKSapTnjxIkrSzPv0UJk4Mi9s2b4ZHH42d\nSJLqlOVBkqSa+OgjePjhUBg+3/Lcty/893/HTiZJdc7yIElSOt54A849F15+OQw4H3ss/PGPcNJJ\n0Lp17HSSlBGWB0mS0tGmDey3H1xyCQwZAnvuGTuRJGWcA9OSJEmS0uI7cZKkwrV2LVRWwre+FfYt\nSJK2y2tLkqTCsnw5TJoUBp6nTIHVq6FrVxg2DDZuhPr1YyeUpKxleZAkFYZPPgkDz08+GUrC174G\nP/1pKA1du8ZOJ0k5IavLQ3l5OcXFxSSTSZLJZOw4kqRc1qIFNGgAN94YXkhq2zZ2IknKOQ5MS5Ik\nSUqLA9OSpNy1eTPMmAGjRsHhh8OmTbETSVJey+prS5Ik/Yd162DatLDlubISFi8OS9pOOglWroS9\n9oqdUJLyluVBkpQbVq+GESO+fCGpc+fw18OGQe/eUORhuiTVNcuDJCk3NGoEiUR4Ienkk8MLSYlE\n7FSSVFAsD5Kk3JBIwH33xU4hSQXNM15JUjybNsH06fCDH0CXLrBsWexEkqTt8ORBkpRZa9bAY4+F\ngedHH4VPP4U2bcLA89q1DjxLUhazPEiSMqO6Gk47Df7+91ASDjwQLrwwzC8cdpgDz5KUAywPkqTM\nKCqC0lL45S/DKUPnzrETSZJqaKd+m+eWW26hQ4cO7L777vTp04eXX355m58dO3YsRUVF1KtXj6Ki\nIoqKimjUqNFOB5YkZalUasef+f3v4fLLLQ6SlKNqXB7uvfdeLrvsMq688kpeeeUVDj74YI4//niW\nLl26zZ9TUlLCwoULv/j64IMPdim0JClLbNwITzwBF10E7drB3LmxE0mS6lCNy8NNN93EhRdeyPDh\nw+natSujR4+mUaNGjBkzZps/J5FI0KJFC1q2bEnLli1p0aLFLoWWJEW0cmV4MvWss6BFCxgwIAw+\nn3IKNGgQO50kqQ7VqDxs3LiRf/7znxx33HFf/FgikeAb3/gGzz///DZ/3qpVq2jfvj3t2rXj5JNP\nZs6cOTufWJIUz5lnQvPmcPrpMGcOXHopvPIKvPce3HwztG8fO6EkqQ7VaGB66dKlbN68mVatWv3b\nj7dq1Yq33nprqz+nS5cujBkzhp49e1JVVcX111/PkUceyezZsyktLd355JKkzOvRA3r3DgPPFgVJ\nKji18tpSKpUikUhs9e/16dOHPn36fPHXffv2pVu3btx+++1ceeWVtfHtJUm1obo6/HF7T6b+z/9k\nJoskKSvVqDw0b96cevXqsWjRon/78cWLF//HacQ2v2FxMb169eLtt9/e4Wc7d+5MIpGgtLT0i1OK\nZDJJMpmsSWxJ0rasXw9PPhkWtlVWwvjxcPTRsVNJkrJUjcpD/fr1Oeyww5g2bRplZWVAOHWYNm0a\nF198cVr/GtXV1bzxxhuccMIJO/zsvHnzaNq0aU0iSpJ25NNPYdKkUBamToVVq2D//cMAdJs2sdNJ\nkrJYja8tjRo1ihEjRnDYYYdxxBFHcNNNN7FmzRq++c1vAjB8+HD23Xdfrr76agB+9atf0adPHzp1\n6sTy5cu57rrr+OCDDzjvvPNq9RciSUrDiBFw993hilLv3vCTn0BZWdj2vI3rp5Ikfa7G5eH0009n\n6dKlXHHFFSxatIhDDjmEqVOnfvH86kcffURx8Zf/ssuWLeOCCy5g4cKF7LXXXhx22GE8//zzdO3a\ntfZ+FZKk9Bx9NPTrByeeCK1bx04jScoxiVQqnZWgmbVixQpKSkqoqqry2pIkpWvt2nB60LBh7CSS\npDxV4yVxkqQssngx3HEHDBsW9i889FDsRJKkPFYrT7VKkjLorbfgkUfCwPPMmeHH+vaFK66AI4+M\nm02SlNcsD5KUS84+G8aNg913h4ED4S9/gSFDIM3nsiVJ2hXOPEhSLnnssbCb4bjjoFGj2GkkSQXG\nkwdJyhYLF0KDBtCs2bY/M3Bg5vJIkrQFB6YlKZZUCubMgWuuCTMLbdrAnXfGTiVJ0jZ58iBJmbRp\nEzz3XBh2fuQReOcdaNwYjj8+vJo0ZEjshJIkbZPlQZIy6fzzw+lC69Zhs/Pvfw/HHutuBklSTnBg\nWpIyadYs2LABDj8cirw5KknKLZ48SFJtSKXgjTdgjz2gQ4dtf+6QQzKXSZKkWuZve0nSztq4EZ58\nEi65BDp2hJ494bbbYqeSJKnOePIgSTVRVQVTpoSB58mTYfly2HffML9QVgbHHBM7oSRJdSarZx4G\nDx5McXExyWSSZDIZO5YkwahRcNNN4fpRWRmcdBL06gWJROxkkiTVuawuDw5MS8o68+dDdTXst1/s\nJJIkZZzXliQJwgtI06fDXnuFl5C2pW3bzGWSJCnLODAtqXAtXw733APl5dCiBQwcGBa1SZKkrfLk\nQVJhmT8fHnwwDDw/80zY+Hz44XD55WF+4aCDYieUJClrWR4kFZbx4+FnPwtbnf/wBzjxxPBakiRJ\n2iEHpiUVlqqqsNm5SZPYSSRJyjmePEjKDwsXwqRJYXahrGzbnyspyVwmSZLyjAPTknJTKgWvvw5X\nXw19+kDr1nDBBTBtWuxkkiTlLU8eJOWWV1+FMWPCwPP778Mee8Dxx8PIkXDCCdC8eeyEkiTlLcuD\npNzyxhvw0EPhatLQoXDMMbDbbrFTSZJUEByYlpRbNm2CevUgkYidRJKkguPJg6T4Nm+G55+HiRNh\nn33gBz/Y9meL/a8tSZJi8Z/CkuJYuRIeeyzMLkyeDEuXQsuW8J3vxE4mSZK2wfIgKbOefRZ+/Wt4\n6inYsAF69IDzzw8zDEccEXYwSJKkrGR5kJRZmzeHuYXrrw8Dzx06xE4kSZLS5MC0JEmSpLRk9f2A\n8vJyysrKqKioiB1F0vYsWgR//SucfHK4giRJkvJSVl9bGj9+vCcPUjZKpWD27DDsXFkJL70UfvzI\nI2HgwLjZJElSncnq8iApC02bBuedF7Y7N24ctjvfcUfY7tyiRex0kiSpDlkeJNVMu3ahKHy+3blh\nw9iJJElShjgwLenfrV4dThQkSZK2kNUD05IyYPNmeO45+PGPoVu3cKIgSZK0FV5bkgrRqlVfbnee\nNOnL7c4nnhheTJIkSdoKy4NUaKZNCzMLGzbAgQe63VmSJKXN8iAVml694LrrwvWkjh1jp5EkSTnE\ngWkpn6xbBx98AF26xE4iSZLykHcUpFy3eHHYszBsGOy9N5x0UuxEkiQpT3ltSco1qRTMmROGnSdO\nhBdeCD/ety9ccYWvJUmSpDpjeZByzYwZcPTRX253HjMmDEC3bBk7mSRJynOWBynX9O0LkydD//5u\nd5YkSRnlzIOUTd55B/7+9+1/pn59GDzY4iBJkjLOkwcpps2bw8zCxInha84caN0aPvrInQuSJCnr\nWB6kTFuzBqZMCWXh0UfDducWLcJ251//GgYMsDhIkqSslNV7HgYPHkxxcTHJZJJkMhk7llQ73nwT\nuncPX2Vl4XWk3r2hXr3YySRJkrYrq8uDS+KUl1IpeP996NAhdhJJkqQa8W6EVFvWrQuvIN144/Y/\nl0hYHCRJUk6yPEi74qvbnZs3hyFD4E9/go0bYyeTJEmqdQ5MSzX12Wdw++1hw/Pn25379IGf/SzM\nL3TvHk4XJEmS8owzD1JNffopdOwIxx0XysKQIW53liRJBcGTB6mm9t47PK9av37sJJIkSRnlzIP0\nuXfegd/9Dr75zR1/1uIgSZIKkCcPKlybN8NLL4XZhcrKsN25QYNwHWn1amjcOHZCSZKkrGJ5UOFZ\nuhR+9KOw3XnJkvBK0le3O++xR+yEkiRJWcnyoMJTUhJOGc49N2x4druzJElSWiwPKjz163/5xKok\nSZLS5sC08sO6dfD3v8PIkXDwwbBpU+xEkiRJeceTB+WuJUtg0iSYOBGmTg1Dzh06hKtIq1eH60mS\nJEmqNZYH5Z6qqrCYbebM8Nd9+sBPfxpKg9udJUmS6ozlQbmnaVPo0SMMPA8ZAq1axU4kSZJUEBKp\nVCoVO8SWVqxYQUlJCVVVVTRt2jR2HGXamjXQqFHsFJIkSdpCVg9Ml5eXU1ZWRkVFRewoqmvvvgs3\n3wzf+EbYu7B8eexEkiRJ2kJWX1saP36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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "interp_timelike_radial = geod.interpolate(solution_key='timelike_radial', interpolation_key='timelike_radial', \n", " verbose=True)\n", "\n", "error_squar_norm_timelike_radial = []\n", "error_e_timelike_radial = []\n", "\n", "i = 0\n", "for (S,TA,RH,TH,PH) in sol_timelike_radial:\n", " P = geod(S, interpolation_key='timelike_radial')\n", " V = geod.tangent_vector_eval_at(S, interpolation_key='timelike_radial')\n", "\n", " squar_norm_timelike_radial = numerical_approx((g.at(P)(V,V)).substitute({b:1}))\n", " e_timelike_radial = numerical_approx((-g.at(P)[0,0]*V[0]).substitute({b:1}))\n", " \n", " if i == 0:\n", " squar_norm_timelike_radial_0 = squar_norm_timelike_radial\n", " e_timelike_radial_0 = e_timelike_radial\n", " \n", " if i == 10:\n", " squar_norm_timelike_radial_0 = squar_norm_timelike_radial\n", " e_timelike_radial_0 = e_timelike_radial\n", "\n", " error_squar_norm_timelike_radial += [(S,squar_norm_timelike_radial - squar_norm_timelike_radial_0)]\n", " error_e_timelike_radial += [(S,e_timelike_radial - e_timelike_radial_0)]\n", " \n", " i += 1\n", "\n", "plot_error_squar_norm_timelike_radial = line(error_squar_norm_timelike_radial)\n", "plot_error_e_timelike_radial = line(error_e_timelike_radial)\n", "\n", "plot_error_squar_norm_timelike_radial.show(title=\"Timelike, radial geodesic: error on conservation of squared norm\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_e_timelike_radial.show(title=\"Timelike, radial geodesic: error on conservation of e\", \n", " ymin=-1e-3, ymax=1e-3)\n", "\n", "geod.plot_integrated(interpolation_key='timelike_radial', ambient_coords=(rh,ta), plot_points=200, style='--')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "deletable": true, "editable": true }, "source": [ "One may thus plot a grid of null and timelike radial geodesics in AdS spacetime:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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Z8NZbYBjErV1DdL/eREeHM+mdPDQdv5YGRRskyel+uvITvbf25vaj24yuM5ph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\naZv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"text/plain": [ "Graphics object consisting of 12 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "S_MAX_NULL = [10, 10, 10, 1]\n", "TH_0_NULL = [0, pi/4, pi/2, 3*pi/4]\n", "\n", "grid = Graphics()\n", "\n", "for (S_MAX,TH_0) in zip(S_MAX_NULL,TH_0_NULL):\n", " params_values_null_radial = {b:1, s_0:0, s_max:S_MAX, ta_0:TH_0, rh_0:1e-3, th_0:pi/3, ph_0:pi/4, \n", " Dta_0:1/cosh(1e-3), Drh_0:1, Dth_0:0, Dph_0:0}\n", "\n", "\n", " sol_null_radial = geod.solve(step=S_MAX/100, parameters_values=params_values_null_radial, \n", " solution_key='null_radial-{}'.format(TH_0))\n", "\n", " interp_null_radial = geod.interpolate(solution_key='null_radial-{}'.format(TH_0),\n", " interpolation_key='null_radial-{}'.format(TH_0))\n", "\n", " grid += geod.plot_integrated(interpolation_key='null_radial-{}'.format(TH_0), ambient_coords=(rh,ta), \n", " plot_points=200, color='green')\n", "\n", "S_MAX_NULL_BACK = [1, 10, 10, 10]\n", "TH_0_NULL_BACK = [pi/4, pi/2, 3*pi/4, pi]\n", "\n", "for (S_MAX,TH_0) in zip(S_MAX_NULL_BACK,TH_0_NULL_BACK):\n", " params_values_null_radial_back = {b:1, s_0:0, s_max:S_MAX, ta_0:TH_0, rh_0:1e-3, th_0:pi/3, ph_0:pi/4, \n", " Dta_0:-1/cosh(1e-3), Drh_0:1, Dth_0:0, Dph_0:0}\n", "\n", "\n", " sol_null_radial = geod.solve(step=S_MAX/100, parameters_values=params_values_null_radial_back, \n", " solution_key='null_radial_back-{}'.format(TH_0))\n", "\n", " interp_null_radial = geod.interpolate(solution_key='null_radial_back-{}'.format(TH_0),\n", " interpolation_key='null_radial_back-{}'.format(TH_0))\n", "\n", " grid += geod.plot_integrated(interpolation_key='null_radial_back-{}'.format(TH_0), ambient_coords=(rh,ta), \n", " plot_points=200, color='green')\n", "\n", "S_MAX_TIMELIKE = [3.13, 3.14, 3.14, 3.19]\n", "DRH_0_TIMELIKE = [0.4, 1, 2.5, 10]\n", "\n", "for (S_MAX,DRH_0) in zip(S_MAX_TIMELIKE,DRH_0_TIMELIKE):\n", " params_values_timelike_radial = {b:1, s_0:0, s_max:S_MAX, ta_0:0, rh_0:1e-3, th_0:pi/3, ph_0:pi/4, \n", " Dta_0:sqrt(DRH_0^2 + 1)/cosh(1e-3), Drh_0:DRH_0, Dth_0:0, Dph_0:0}\n", "\n", "\n", " sol_timelike_radial = geod.solve(step=S_MAX/100, parameters_values=params_values_timelike_radial, \n", " solution_key='timelike_radial-{}'.format(DRH_0))\n", "\n", " interp_timelike_radial = geod.interpolate(solution_key='timelike_radial-{}'.format(DRH_0),\n", " interpolation_key='timelike_radial-{}'.format(DRH_0))\n", "\n", " grid += geod.plot_integrated(interpolation_key='timelike_radial-{}'.format(DRH_0), ambient_coords=(rh,ta), \n", " plot_points=200, style='--')\n", "\n", "grid.show()" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.1.beta2", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }