{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Geodesics in Schwarzschild spacetime\n", "\n", "This notebook aims at recovering some geodesics of Schwarzschild spacetime using numerical tools implemented in the SageMath class **IntegratedGeodesic**, within the [SageManifolds](https://sagemanifolds.obspm.fr) project (version 1.3, as included in SageMath 8.3).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.3/SM_Schwarzschild_geod.ipynb) to download the notebook file (ipynb format). To run it, you must start SageMath within the Jupyter notebook, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 8.2 is required to run this notebook:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.3, Release Date: 2018-08-03'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First set up the notebook to display mathematical objects using LaTeX rendering:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spacetime manifold\n", "\n", "To set the Schwarzschild spacetime, declare a 4-dimensional Lorentzian manifold and a non-negative parameter $m$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "Schw = Manifold(4, 'Schw', latex_name=r'\\mathcal{Schw}', \n", " structure='Lorentzian')\n", "m = var('m') ; assume(m >= 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the Boyer-Lindquist coordinates on the union of two subregions $\\mathcal{R}_{\\mathrm{I}}$ and $\\mathcal{R}_{\\mathrm{II}}$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "regI = Schw.open_subset('R_I', r'\\mathcal{R}_{\\mathrm{I}}')\n", "regII = Schw.open_subset('R_II', r'\\mathcal{R}_{\\mathrm{II}}')\n", "regI_II = regI.union(regII)\n", "BL. = regI_II.chart(r't r:(0,+oo) th:(0,pi):\\theta ph:\\phi')\n", "BL_I = BL.restrict(regI, r>2*m)\n", "BL_II = BL.restrict(regII, r<2*m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally set the Lorentzian metric of Schwarzschild spacetime:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{2 \\, m}{r} - 1 \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( -\\frac{1}{\\frac{2 \\, m}{r} - 1} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "g = (2*m/r - 1) dt*dt - 1/(2*m/r - 1) dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = Schw.metric()\n", "g[0,0], g[1,1] = -(1-2*m/r), 1/(1-2*m/r)\n", "g[2,2], g[3,3] = r^2, (r*sin(th))^2\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Geodesics in Boyer-Lindquist coordinates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining the geodesic" ] }, { "cell_type": "markdown", "metadata": {}, "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": {}, "outputs": [], "source": [ "affine_param = var('s s_0 s_max')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, declare the starting point of the geodesic:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "initial_pt_coords = var('t_0 r_0 th_0 ph_0') ; assume(r_0 > 2*m)\n", "p_0 = regI.point(initial_pt_coords, name='p_0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Declare the initial tangent vector:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "initial_tgt_vec_comps = var('Dt_0 Dr_0 Dth_0 Dph_0')\n", "v_0 = Schw.tangent_space(p_0)(initial_tgt_vec_comps)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parametrised geodesic may now be initialised:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "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, Dr_0, Dt_0, Dth_0, m, ph_0, r_0, s_0, s_max, t_0, th_0].\n" ] } ], "source": [ "geod = Schw.integrated_geodesic(g, affine_param, v_0, verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the system of the geodesic equations:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Geodesic in the 4-dimensional Lorentzian manifold Schw equipped with Lorentzian metric g on the 4-dimensional Lorentzian manifold Schw, and integrated over the Real interval (s_0, s_max) as a solution to the following geodesic equations, written with respect to Chart (R_I_union_R_II, (t, r, th, ph)):\n", "\n", "Initial point: Point p_0 on the 4-dimensional Lorentzian manifold Schw with coordinates [t_0, r_0, th_0, ph_0] with respect to Chart (R_I_union_R_II, (t, r, th, ph))\n", "Initial tangent vector: Tangent vector at Point p_0 on the 4-dimensional Lorentzian manifold Schw with components [Dt_0, Dr_0, Dth_0, Dph_0] with respect to Chart (R_I_union_R_II, (t, r, th, ph))\n", "\n", "d(t)/ds = Dt\n", "d(r)/ds = Dr\n", "d(th)/ds = Dth\n", "d(ph)/ds = Dph\n", "d(Dt)/ds = 2*Dr*Dt*m/(2*m*r - r^2)\n", "d(Dr)/ds = -(4*Dth^2*m^2*r^3 - 4*Dth^2*m*r^4 + Dth^2*r^5 - 4*Dt^2*m^3 + 4*Dt^2*m^2*r + (Dr^2 - Dt^2)*m*r^2 + (4*Dph^2*m^2*r^3 - 4*Dph^2*m*r^4 + Dph^2*r^5)*sin(th)^2)/(2*m*r^3 - r^4)\n", "d(Dth)/ds = (Dph^2*r*cos(th)*sin(th) - 2*Dr*Dth)/r\n", "d(Dph)/ds = -2*(Dph*Dth*r*cos(th) + Dph*Dr*sin(th))/(r*sin(th))\n", "\n" ] } ], "source": [ "sys = geod.system(verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing numerical solutions\n", "\n", "#### Timelike geodesics\n", "\n", "##### Bounded orbit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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 with squared norm equal to -1. This way, the curve parameter `s` not only is an affine parameter of the (timelike) geodesic, but it actually is the proper time along it (up to numerical roundings)." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "params_values_bounded = {m:1, s_0:0, s_max:1500, t_0:0, r_0:8, th_0:pi/2, ph_0:1e-12, \n", " Dt_0:sqrt(80.81)/(4*sqrt(3)), Dr_0:0, Dth_0:0, Dph_0:4.1/64}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then integrate the geodesic for such values of the parameters:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Schw.default_chart().valid_coordinates(*p_0.coord())" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing numerical integration with method 'rk4_maxima'...\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_bounded_equatorial' (if this key already referred to a former numerical solution, such a solution was erased).\n" ] } ], "source": [ "sol_bounded = geod.solve(step=4, parameters_values=params_values_bounded, \n", " solution_key='timelike_bounded_equatorial', verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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, up to a rotation of the system of polar coordinates, any geodesic in Schwarzschild spacetime is known to have constant coordinate $\\theta$ equal to $\\pi/2$ (which is why it was suggested above to set the initial condition on $\\theta$ to $\\pi/2$).\n", "In such a situation, energy $e$ and angular momentum $l$ per unit mass, defined as follows, are also conserved along a geodesic of Schwarzschild spacetime:\n", "\n", "$$e = \\left( 1 - \\frac{2m}{r} \\right) \\dot{t}$$\n", " \n", "$$l = r^{2} \\dot{\\phi}$$\n", "\n", "Therefore, using an interpolation of the previous numerical solution, one may check that these three quantities are indeed conserved along the numerical solution previoulsy computed (not to be disturbed by initial edge effects, the reference value used to check conservations of the various quantities is updated after 10 steps):" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing cubic spline interpolation by default...\n", "Interpolation completed and associated with the key 'timelike_bounded_equatorial' (if this key already referred to a former interpolation, such an interpolation was erased).\n" ] }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interp_bounded = geod.interpolate(solution_key='timelike_bounded_equatorial', \n", " interpolation_key='timelike_bounded_equatorial', \n", " verbose=True)\n", "\n", "error_squar_norm_bounded = []\n", "error_e_bounded = []\n", "error_l_bounded = []\n", "\n", "i = 0\n", "for (S,T,R,TH,PH) in sol_bounded:\n", " P = geod(S, interpolation_key='timelike_bounded_equatorial')\n", " V = geod.tangent_vector_eval_at(S, interpolation_key='timelike_bounded_equatorial')\n", "\n", " squar_norm_bounded = numerical_approx((g.at(P)(V,V)).substitute({m:1}))\n", " e_bounded = numerical_approx((-g.at(P)[0,0]*V[0]).substitute({m:1}))\n", " l_bounded = numerical_approx((g.at(P)[3,3]*V[3]).substitute({m:1}))\n", " \n", " if i == 0:\n", " squar_norm_bounded_0 = squar_norm_bounded\n", " e_bounded_0 = e_bounded\n", " l_bounded_0 = l_bounded\n", " \n", " if i == 10:\n", " squar_norm_bounded_0 = squar_norm_bounded\n", " e_bounded_0 = e_bounded\n", " l_bounded_0 = l_bounded\n", "\n", " error_squar_norm_bounded += [(S,squar_norm_bounded - squar_norm_bounded_0)]\n", " error_e_bounded += [(S,e_bounded - e_bounded_0)]\n", " error_l_bounded += [(S,l_bounded - l_bounded_0)]\n", " \n", " i += 1\n", "\n", "plot_error_squar_norm_bounded = line(error_squar_norm_bounded)\n", "plot_error_e_bounded = line(error_e_bounded)\n", "plot_error_l_bounded = line(error_l_bounded)\n", "\n", "plot_error_squar_norm_bounded.show(title=\"Timelike geodesic - Bounded orbit: error on conservation of squared norm\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_e_bounded.show(title=\"Timelike geodesic - Bounded orbit: error on conservation of e\", \n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_l_bounded.show(title=\"Timelike geodesic - Bounded orbit: error on conservation of l\",\n", " ymin=-2e-3, ymax=2e-3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The curves are indeed constant with negligible numerical variations, the jolts in the middle being correlated with radial coordinate $r$ reaching a minimum.\n", "The jolts get smaller if one uses a shorter step of integration when calling method `solve`.\n", "\n", "One may finally plot the spatial part of the geodesic.\n", "To do so, start with defining the 3-dimensional Euclidean space with Cartesian coordinates:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "R3 = Manifold(3, 'R3', start_index=1)\n", "cart. = R3.chart()\n", "origin = R3.point((0,0,0), name='O')\n", "plot3D_origin = origin.plot(size=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then define the mapping converting the spatial part of Boyer-Lindquist coordinates (i.e. the polar coordinates) into the Cartesian coordinates:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "BL_spatial_coords = Schw.diff_map(R3,{(BL, cart): [r*sin(th)*cos(ph), r*sin(th)*sin(ph),\n", " r*cos(th)]})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This allows to plot the spatial part of the geodesic:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": false }, "outputs": [], "source": [ "plot3D_projected_geod_bounded = geod.plot_integrated(interpolation_key='timelike_bounded_equatorial',\n", " mapping=BL_spatial_coords, \n", " plot_points=500, thickness=2,\n", " display_tangent=True, \n", " plot_points_tangent=30, scale=8, \n", " width_tangent=1, label_axes=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the event horizon:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "plot3D_event_horizon = BL.plot(chart=cart, mapping=BL_spatial_coords, \n", " fixed_coords={t:0, r:2}, ranges={ph:(0,2*pi)}, \n", " number_values=15, color='yellow', label_axes=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display all graphics:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(plot3D_projected_geod_bounded + plot3D_event_horizon + plot3D_origin).show(viewer='threejs',\n", " online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, one notices the advance of the periastron of such a bounded orbit.\n", "\n", "##### Circular case\n", "\n", "Schwarzschild spacetime admits circular orbits.\n", "The unique timelike geodesic (still parametrised with proper time) inducing a stable circular orbit with same angular momentum as that of the geodesic considered above is obtained with the following initial conditions:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "params_values_circular = {m:1, s_0:0, s_max:500, t_0:0, r_0:(16.81 + 4.1*sqrt(4.81))/2, \n", " th_0:pi/2, ph_0:0, Dt_0:1.1415, Dr_0:0, Dth_0:0, \n", " Dph_0:16.4/(16.81+4.1*sqrt(4.81))^2}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve, interpolate and plot the orbit corresponding to such values of the parameters:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing numerical integration with method 'rk4_maxima'...\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_circular_equatorial' (if this key already referred to a former numerical solution, such a solution was erased).\n", "Performing cubic spline interpolation by default...\n", "Interpolation completed and associated with the key 'timelike_circular_equatorial' (if this key already referred to a former interpolation, such an interpolation was erased).\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sol_circular = geod.solve(step=4, parameters_values=params_values_circular, \n", " solution_key='timelike_circular_equatorial', verbose=True)\n", "interp_circular = geod.interpolate(solution_key='timelike_circular_equatorial', \n", " interpolation_key='timelike_circular_equatorial', \n", " verbose=True)\n", "\n", "error_squar_norm_circular = []\n", "error_e_circular = []\n", "error_l_circular = []\n", "error_r_circular = []\n", "\n", "i = 0\n", "for (S,T,R,TH,PH) in sol_circular:\n", " P = geod(S, interpolation_key='timelike_circular_equatorial')\n", " V = geod.tangent_vector_eval_at(S, interpolation_key='timelike_circular_equatorial')\n", "\n", " squar_norm_circular = numerical_approx((g.at(P)(V,V)).substitute({m:1}))\n", " e_circular = numerical_approx((-g.at(P)[0,0]*V[0]).substitute({m:1}))\n", " l_circular = numerical_approx((g.at(P)[3,3]*V[3]).substitute({m:1}))\n", " \n", " if i == 0:\n", " squar_norm_circular_0 = squar_norm_circular\n", " e_circular_0 = e_circular\n", " l_circular_0 = l_circular\n", " R_0 = R\n", "\n", " error_squar_norm_circular += [(S,squar_norm_circular - squar_norm_circular_0)]\n", " error_e_circular += [(S,e_circular - e_circular_0)]\n", " error_l_circular += [(S,l_circular - l_circular_0)]\n", " error_r_circular += [(S,R - R_0)]\n", " \n", " i += 1\n", " \n", "plot_error_squar_norm_circular = line(error_squar_norm_circular)\n", "plot_error_e_circular = line(error_e_circular)\n", "plot_error_l_circular = line(error_l_circular)\n", "plot_error_r_circular = line(error_r_circular)\n", "\n", "plot_error_squar_norm_circular.show(title=\n", " \"Timelike geodesic - Circular orbit: error on conservation of squared norm\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_e_circular.show(title=\"Timelike geodesic - Circular orbit: error on conservation of e\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_l_circular.show(title=\"Timelike geodesic - Circular orbit: error on conservation of l\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_r_circular.show(title=\"Timelike geodesic - Circular orbit: error on conservation of r\",\n", " ymin=-1e-3, ymax=1e-3)\n", "\n", "plot3D_projected_geod_circular = geod.plot_integrated(interpolation_key='timelike_circular_equatorial',\n", " mapping=BL_spatial_coords, \n", " plot_points=250, thickness=2,\n", " display_tangent=True, \n", " plot_points_tangent=10, scale=8,\n", " width_tangent=1, label_axes=False)\n", "\n", "(plot3D_projected_geod_circular + plot3D_event_horizon + plot3D_origin).show(viewer='threejs',\n", " online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second graph, which displays the evolution of radial coordinate $r$, does confirm that the orbit is circular, up to negligible oscillations.\n", "\n", "##### Unbounded trajectory\n", "\n", "In Schwarzschild spacetime, geodesics with sufficiently high radial velocity or angular momentum may induce unbounded trajectories.\n", "An example of such a geodesic (still parametrised with proper time) which has same angular momentum as that of the geodesics considered above is provided below:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing numerical integration with method 'rk4_maxima'...\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_unbounded_equatorial' (if this key already referred to a former numerical solution, such a solution was erased).\n", "Performing cubic spline interpolation by default...\n", "Interpolation completed and associated with the key 'timelike_unbounded_equatorial' (if this key already referred to a former interpolation, such an interpolation was erased).\n" ] }, { "data": { "image/png": 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SpWzfvn0e7WrWrOkR0n/66Sfz8/PzePGYmR07dsxiYmLsnnvuMTOzQ4cOmSR74YUX8tznC0P63//+9xzDSGEraEivU6eOZWRkuJd/8cUXJsnjA0RqaqpJshdffNFjnWPGjDFJtmrVKjPLOglKsgkTJni0e+edd0ySvfrqq+5llxrS//d//9ej3YQJE0yS7d2718zMvv76a5PkdaJ6++23TZLHOh966CELDQ21H3/80aPt888/b5Lc/XXatGkmyf797397tPvzn/980ZBuZvbPf/7T68NotubNm5skW7JkSZ7ryMzMtLNnz9qKFStMkm3atMl934UhPb992cysatWqVrVqVfv9999z3fZzzz3n9YHW7L/H+sLnZO3atSbJnnrqqXztZ/Pmza1+/foeyx5++GELDw/3eH0PGzbMfH193f0sNytXrsyxn/7www8WGBjoUVdiYqJJ8ggh2eLi4szf398jWJmZzZ8/3yTZpEmTPJZn97E33njjouvIyaFDhywwMNA6d+7ssXz37t0WEBBgPXr0cC9LSUnxer8wM2vbtq3deOONeW5n586d5uPj4/FauBK1/OUvf7GyZcvmWVvv3r0tPDzcI8CZmY0fP95cLpft2LHDvQ+SrHr16nb27FmPtnPnzjVJtnTpUveys2fPWvny5e3ee+/NddsZGRl29uxZa968uXXp0sW9fO/evSbJnn32Wa/HXBg4r9RzuHXrVpNk/fv391j+2WefmSQbNmyYe1n2h9sjR47kuc59+/aZJJsyZUqubbZs2WKS7PHHH/dY/tZbb5mkAof082Wf65YsWeJxHjb77zH7+9//7vGYY8eOWUREhP3P//yPx/KMjAy78cYbrUmTJu5lN910k8XHx3tcLDp69KiVLl063yHd5XLZV1995VFzjRo1rGPHju5ljz32mLlcLvvyyy89Hv/nP//ZXC6X+5yQV1/ODukX7lffvn1Nkg0cONBjeVJSkpUrV+6i+5BfJX64S16SkpI8bteqVUsul0sdOnRwL/Pz89P111+vH3/80b1s/vz5ql27turXr6+MjAz3T7t27XIcOpJfY8aMUc+ePTV+/Hi9+OKL8vH579OzevVq/fbbb0pNTfXYZmZmptq3b69169bl+SuWFStWqHbt2l7jtLt27epxO7/bOXHihNauXau7777bY7YRX19fde/eXXv27HH/anHZsmVq3bq1ypcv79Hu3nvv9dj2J598ooyMDPXo0cNj20FBQWrevLn7uEZGRqpq1ap67rnnNGnSJG3YsEGZmZkXPb7/+c9/FBQU5B7KkF9m5lHPhcMwCkvHjh3l6+vrvl23bl1J8uh72VJSUjxu33fffZKyjrUk95eoL5xJpUuXLgoJCcn3EKmcdO7c2eP2hXVm13Bhjffcc4/Xr17nz5+vli1bKjY21uP4Zr8GV6xY4V5nWFiY17az9/tylSlTRq1atfJa/v333+u+++5TTEyMfH195e/vr+bNm0uSvv7661zXl9++/O233+q7775T7969C/RlsuxjfeHzfPPNN6tWrVpez3Nu+/nII49o48aN7mEG6enpmjlzplJTUz1e39nDkBITE/Osa/78+fLx8VFKSorH/sfFxalOnTpe58jo6GivLwRmq1+/vtcX7XPr38nJyQoKCvLa75zWkZPVq1fr9OnTXuutUqWKmjdv7rVeX19fdezY0WNZ3bp1c3zNnm/hwoXKzMxUnz59rmgtN998sw4dOqSUlBR98MEHOnz4sNd258+fr9atWysmJsbrNWlm7tdktttvv93rdZ2UlKTo6GjNmDHDvezjjz/W/v37vc6/U6dOVYMGDRQUFCQ/Pz/5+/trxYoVeb6+8nKlnsPc+mCTJk1UrVq1Ap1jo6OjVaVKFY0fP14vvPCCNm7c6PXeltv5NTk52SMzXKpdu3apa9euKl++vPtc17p1a0k5n+vuvPNOj9urVq1SWlqaV3YwM7Vv315r167VqVOnlJ6ervXr1+vuu+/2GO8dERHh9TzkJS4uTn/4wx/ct10ul+rUqePxvC1dulR16tTRTTfd5PHYnj17yszcxzJbTn05W055UZJXzbVq1dKBAwd06tSpfO9LXq7KL44Wlgu/wBEQEKDg4GCvN8uAgAClp6e7b+/fv1+7du2Sv79/just6FSKs2bNUlxcnJKTk73u279/vyTp7rvvzvXxv/32m0JCQnK87/Dhw0pISPBafn5wvpTtuFwumZl7rOD5YmNj3dvM/jcmJsar3YXLsrf9xz/+McftZp+AXC6XlixZolGjRmnChAkaNGiQIiMjlZKSojFjxigsLCzHxx88eFCxsbGXfCJ766231KtXL49ldsG4t/Nlv8jPH795voyMjBz7TlRUlMft7BPY77//7rX+C9tmH8vzj7mfn5/XF6pcLpdiYmJyfHPOr4vVmb3uC5/fnOrev3+/Pvzww4u+lg4fPuzVV3PaRkHl1I+PHz+uZs2aKSgoSKNHj1b16tUVHBysn3/+WXfeeafX83K+/PblgwcPSlKBv3Safaxzex1eGDRyaidlvTlVqVJFU6dOVWJiot58802dOHEizxCZl/379yszMzPXqeaqV6+er7pyu+/w4cMKDAxUmTJlPJb7+PiofPnyXv07r/VfuN7c2sfGxmrlypUey0JDQxUQEOCxLDAwMM++IeXveS+KWnr27KnMzEy9/vrruvPOO2Vm+uMf/6gxY8a4A9mBAwc0b968fL+/5VSfv7+/unXrpunTp2vKlCkKDw/Xm2++qfj4eLVp08bdbsKECRo8eLD+93//V6NHj1bZsmXl6+urp556St9//32uxyYvV+o5vNh2ss8Bl8LHx0fLli3TqFGjNG7cOA0YMEBRUVHq1q2bRo8erdDQ0FzPrwEBAV6vh/xKT09Xs2bNFBoaqrFjx6p69eoqVaqUfvjhB3Xp0sXrWISHh3tljez9veOOO3LdzpEjR3T69GmZWb4yQV4ufC+RvJ+3w4cPq2bNml7tLswo2fI6T+SUF/NafurUqUKZxeeaDukFVbZsWZUqVUpvvPFGrvcXxIIFC3TvvfeqWbNmWrJkiSpXruy1zpdeeinX2WFyCjHZoqKicjxpXPjFu/xu5+zZs/Lx8dHevXu97s/+0kz2uqKionL8gl9u2/7Xv/7lse85qVy5sv7v//5PUtbVyHfffVcjRozQmTNn9Morr+T4mOjoaK1atUqZmZmXFNQ7deqkdevW5bt99vPwyy+/5Hj/L7/8kudzdTEZGRk6fPiwx0kq+1hmL4uKilJGRoYOHjzoEdTNTPv27fMIj4GBgTp9+rTXdgoa5LNr2Ldvn+Li4rzqPl/ZsmVVt27dXL/Il30yjYqKyvGLp/n54mh+5PSlz6VLl+rXX3/V8uXL3VfPJeVrrvL89uXs56agczxnH+u9e/d6Bb5ff/3V61yU21zuPj4+6tOnj5566ilNnDhRL7/8slq3bq0aNWoUqK6yZcvKx8dHq1atyjHsXfjmldcc8zndFxUVpdOnT+vIkSMewSQzM1P79+9Xs2bN8r3+C9crKdfzWmHNb33+855bMCiKWlwul3r37q3evXvr+PHjWrFihYYPH66kpCTt3LlT8fHxioqK0s0335zjFz8lebyms9eZk169emny5Ml69913dccdd2j+/Pl64oknPM69s2bNUps2bTR16lSPx55/UexSXann8PztXBguf/311wKf46tUqeLOFjt27NA777zj/g3WlClTPM6v52/jzJkzOnLkiMe6goKClJmZqYyMDI8rxBd+0Fq8eLH27dunVatWefyWLLcLjjk959nH9eWXX8714kTZsmX1+++/y+Vy5SsTXK6oqKh8ZZRsRfm3Lgrqmh7uUlBJSUn67rvvFBUVpYYNG3r9FHQe5sqVK2vlypUKDAxUs2bNtHPnTvd9iYmJKl26tLZv357jNhs2bOh1NeB8zZs319atW7V9+3aP5XPmzPG4nd/thISE6JZbbtHcuXM9PrlmZmZq1qxZio+Pd18ta9mypZYsWeLxIeHcuXN65513PLbdrl07+fn56bvvvst12zmpXr26hg4dqjp16mj9+vW5HoMOHTro1KlTl/yHrXJ6nvPSqFEjhYaGeu2flDVf97Zt2zyuJhXE22+/7XH7H//4hyS5Z7PJvio2a9Ysj3bvvfeeTpw44b5fynpT2Lx5s0e7pUuX6vjx4wWqLbuGC2t89913vYYKJSUlaevWrapatWqOz3d2SG/ZsqWOHTumDz74wOPx2ft9Mbn9ViIv2SfsC6fgmj59+kUfm9++XL16dVWtWlVvvPFGjh+ULlZ/9tCVC5/ndevW6euvv/Z4ni/mgQceUEBAgFJSUrRjxw717ds334+9UFJSkjIzM7V3794c97127doFXreUe/9+9913derUqUva7/MlJiYqMDDQa70//fSTVqxYUeD1Xqhdu3by8fHRtGnTiq2W0NBQdezYUUOGDNGpU6fc7w1JSUnavHmzqlWrluNzl9/fSmQPM5gxY4befvttnT171us3ki6Xy+v1tWHDBq+LIpfy+r1Sz2Fur73PP/9cO3fuLJTt1KhRQ8OGDdMNN9zgfm9r2bKlJO/z65w5c7yGxlSpUkVm5jEzjJQ1s8r5Ludcl61Zs2YKDw/X119/nes5z9/fX+Hh4frDH/6g9957z+Ocl5aWluPMcJejdevW2rJli9f729///nf5+Pi4j6WTcSW9AB599FG99957uvXWWzVgwADVrVtXmZmZ+umnn7Rw4UINGjRIt9xyS4HWXaFCBa1YsULt2rXTrbfeqkWLFql27doKDQ3VSy+9pNTUVP3222+6++67Va5cOR08eFCbNm3SwYMH8zzhP/roo3rjjTfUoUMHjRo1SuXLl9c//vEPffPNN5L+++v3S9nOuHHjdNttt6lly5Z67LHHFBAQoJdffllbt27V7Nmz3S/8oUOH6oMPPlCrVq00bNgwBQcHa+rUqV5j6KtUqaJRo0bp6aef1vfff6/27durTJky2r9/v7744guFhIRo5MiR2rx5s/r27asuXbqoWrVqCggI0NKlS7V582Y9+eSTuR6Drl27asaMGfrLX/6iHTt2qGXLlsrMzNTatWtVq1atHIcZFURYWJhGjhypQYMGKTMzU/fee6/KlCmjLVu2aOzYsapcubL69+9f4PUHBARo4sSJOn78uP74xz9q9erVGj16tDp06KCmTZtKkm677Ta1a9dOgwcPVnp6uhITE7V582YNHz5cDRo0UPfu3d3r6969u5555hkNGzZMzZs31/bt2zVlyhRFREQUqL5atWqpW7dueuGFF+Tv7682bdpo69atev755xUeHu7RdtSoUVq0aJGaNGmi/v37q0aNGjp16pR++OEHffzxx3rllVcUHx+vHj16aPLkyerRo4fGjBmjatWq6eOPP9Ynn3ySr5qyQ+Grr76qsLAwBQUFKSEhIcdfmWZr0qSJypQpo7/85S8aPny4/P399fbbb2vTpk0X3V5++7KUNSa3U6dOatSokQYMGKBKlSrpp59+0ieffOJ+I65Tp44k6cUXX1Rqaqr8/f1Vo0YN1ahRQw8++KBeeukl+fj4qEOHDvrhhx/0zDPPqGLFihowYEC+jo8klS5dWj169NC0adNUuXJlderUyavN8OHDNWbMGK1YsSLPcenNmzfX/fffrx49emjt2rW69dZbFRwcrL1792rlypVq0KCBe5rFgujQoYPatGmjxx57TEePHlXjxo21adMmDR8+XA0bNizwdxUiIyP19NNPa9iwYerVq5fuvfdeHTx4UCNGjFBwcLDXVIUFVbVqVQ0ePFjjxo3TyZMndc899yg8PFzbtm3T0aNHNXz48CKppVevXgoPD1diYqJiYmK0d+9ejR07VmXKlHGP2x09erSWLFmiJk2aqF+/fqpRo4Z+//137d69Wx999JHeeOONfA9LuP/++9WnTx/99NNPuvXWW72+F5CUlKRx48Zp1KhRatq0qb755hv3FHjnK1OmjOLi4jRv3jy1aNFCZcqUUXR0dI6/pbpSz+GNN96o+++/X5MnT5aU9cFr9+7deuaZZwp8jl+/fr0GDhyou+++W9WqVZO/v78WL16sbdu2ueuuXbu2kpOTNXGHC7OdAAAgAElEQVTiRPn6+qpVq1basmWLJk2a5DXUMykpSaVLl1avXr00cuRI+fj46I033vC6uty0aVOVLl1aDz74oIYPHy5fX1/NnDlT27Zty3ft4eHh+tvf/qb7779fhw4d0l133aXo6GgdOHBAmzZt0pEjRzRlyhRJWX+AMikpSW3bttXAgQN19uxZjRs3TmFhYTp27NglH7fcDBo0SLNmzXLnnooVK+rDDz/U9OnT1b9/f1133XWFtq0iU2hfQS1GBZ3d5fzpyfJaT/Pmzb2+6X38+HEbOnSo1ahRwwICAiwiIsLq1KljAwYM8JjFpCBTMJplfdM5MTHRIiMjPWYJWbFihXXs2NEiIyPN39/f4uLirGPHjvbPf/4zz2NklvVt9DZt2lhQUJBFRkZa79693d8IP3+mikvZzsqVK61Vq1YWEhJipUqVskaNGtmHH37ote3PPvvMGjVqZIGBgRYTE2OPP/64vfrqqznOWPH+++9by5YtLTw83D3V09133+2e/nH//v3Ws2dPq1mzpoWEhFhoaKjVrVvXJk+e7DE7yoWzu5iZ/f777zZs2DCrVq2aBQQEWFRUlLVq1cpWr1590eN3qd59911r2rSphYWFmZ+fn1WqVMkefvhhj/5h9t8+8dxzz3mtQxfMvJLdRzdv3mwtWrSwUqVKWWRkpD388MN2/Phxr30dPHiwVa5c2fz9/a1ChQr28MMPe80wcPr0aXviiSesYsWKVqpUKWvevLlt3Lgx19ldLpy1ZtmyZV4zp5w+fdoGDRpk5cqVs6CgIGvUqJGtWbPGa51mZgcPHrT+/ftbQkKC+fv7W2RkpN1000329NNPe+zTnj177K677rLQ0FALCwuzu+66y1avXp2v2V3MzF544QVLSEgwX19fj8fk9PrOtnr1amvcuLEFBwdbdHS0PfDAA7Z+/fpcX8MXulhfzrZmzRrr0KGDRUREWGBgoFWtWtVrdpwhQ4ZYbGys+fj4eBzvc+fO2V//+lerXr26+fv7W9myZa1bt25eMzfktZ/Zli9fbpJs/PjxOd5/KVMwZmZm2muvvWY333yzBQcHW6lSpez666+31NRUW79+vbtdYmKi1atXL8d1xMXF2e23357jfSdOnLDHH3/cKlWqZP7+/hYbG2t9+vTxmLL0YuvIzfTp061OnToWEBBgpUuXtjvuuMO+/vprjzYpKSkWERHh9djcZtTIyZtvvmkNGza0oKAgCwsLsz/84Q/21ltvFVktb7zxhrVs2dLKly9vAQEBFhsba8nJybZ161aPx+3fv9/69etnVapUcb8mGzZsaEOHDrWTJ0+a2X9nxJg8eXKu+/fbb79ZUFBQrq/RU6dO2cCBAy02NtaCgoLspptusg8++MBSUlKsatWqHm0XLlxo9erVs8DAQI9ZTHKbqeRKPIcZGRk2duxYq1atmvu11717d/vll1+81qd8zO6yd+9eS01NtRo1alhISIiFhYVZvXr17MUXX/SY7e3UqVM2YMAAi46OtqCgIGvSpImtXbvW4uLiPGZ3Mcs6tzRq1MhCQkIsPj7eRo0aZdOnT/c6ZqtWrbJGjRpZcHCwlStXzh588EFbt26dSbKZM2de9JhlW7ZsmXXo0MHKlCljAQEBFh8fb0lJSR7TWJuZzZs3z2rXrm3+/v5WuXJle+655/J93HM7Z+TUb3bv3m1du3a1qKgo8/f3txo1atjEiRM9pgfNqy9nz+4yb948j+XZ/W7Dhg0ey/P7XOeXyyyPb8ChxHvwwQc1e/ZsHT58OM/hMgByN2DAAM2cObPAXxp3ikGDBmnatGn6+eef8/wtAwDniY+PV/v27fX6668XdykoJAx3uYaMGjVKsbGxuu6663T8+HHNnz9fr7/+uoYOHUpABwrgwIEDWrNmjebOnavGjRsXdzkF9vnnn+vbb7/Vyy+/rIceeoiADgAOQEi/hvj7++u5557Tnj17lJGRoWrVqmnSpEl65JFHirs04Kr08ccfq2/fvmrUqJFefPHF4i6nwBo3bqzg4GAlJSXl+SfLAQBXDsNdAAAAAIdhCkYAAADAYQjpAAAAgMOUmJBuZkpPT8/zz7UDAAAAV4MSE9KPHTumiIiIQp0IHwAAACgOJSakAwAAACUFIR0AAABwGEI6AAAA4DCXHdI//fRTderUSbGxsXK5XHr//fcvu6hVq1YpMTFRUVFRKlWqlGrWrKnJkydf9noBAACAq8Fl/8XREydOqF69eurVq5fuuuuuwqhJISEh6tu3r+rWrauQkBCtWrVKDz30kEJCQvTggw8WyjYAAAAApyrUvzjqcrk0b9483XHHHe5lZ86c0dChQ/X222/r6NGjql27tv7617+qRYsWl7TuO++8UyEhIZo5c2aO96enpysiIkJpaWkKDw+/nN0AAAAAilWRj0nv1auXPvvsM82ZM0ebN29Wly5d1L59e+3cuTPf69iwYYNWr16t5s2bF2GlAAAAgDNc9nCXvHz33XeaPXu29uzZo9jYWEnSY489pgULFmjGjBkaO3Zsno+Pj4/XwYMHlZGRoREjRuiBBx4oynIBAAAARyjSkL5+/XqZmapXr+6x/PTp04qKipIkhYaGupd369ZNr7zyivv2ypUrdfz4cX3++ed68skndf3116tr165FWTIAAABQ7Io0pGdmZsrX11dfffWVfH19Pe7LDucbN250L7twLHlCQoIkqU6dOtq/f79GjBhx0ZCenJwsPz/P3eratSvhHgAAAFeNIg3pDRo00Llz53TgwAE1a9YsxzbXX399vtZlZjp9+vRF282ZM4cvjgIAAOCqdtkh/fjx49q1a5f79u7du7Vx40ZFRkaqevXqSklJUY8ePTRx4kQ1aNBAhw4d0tKlS1WnTh396U9/ynGdU6dOVaVKlVSzZk1JWfOmP//88+rXr9/llgsAAAA43mWH9C+//FItW7Z03x44cKAkKTU1VW+++aZmzJih0aNHa9CgQfrll18UFRWlxo0b5xrQpaxhMkOGDNHu3bvl5+enqlWravz48XrooYcut1wAAADA8Qp1nvTixDzpAAAAKCmKfJ50AAAAAJeGkA4AAAA4DCEdAAAAcBhCOgAAAOAwhHQAAADAYQjpAAAAgMMQ0gEAAACHIaQDAAAADkNIBwAAAByGkA4AAAA4DCEdAAAAcBhCOgAAAOAwhHQAAADAYQjpAAAAgMMQ0gEAAACHIaQDAAAADkNIBwAAAByGkA4AAAA4DCEdAAAAcBhCOgAAAOAwhHQAAADAYUpcSE9OTlbnzp01e/bs4i4FAAAAKBCXmVlxF1EY0tPTFRERobS0NIWHhxd3OQAAAECBlbgr6QAAAMDVjpAOAAAAOAwhHQAAAHAYQjoAAADgMIR0AAAAwGEI6QAAAIDDENIBAAAAhyGkAwAAAA5DSAcAAAAchpAOAAAAOAwhHQAAAHAYQjoAAADgMIR0AAAAwGEI6QAAAIDDENIBAAAAhyGkAwAAAA5DSAcAAAAchpAOAAAAOAwhHQAAAHAYQjoAAADgMIR0AAAAwGEI6QAAAIDDENIBAAAAhyGkAwAAAA5T4kJ6cnKyOnfurNmzZxd3KQAAAECBuMzMiruIwpCenq6IiAilpaUpPDy8uMsBAAAACqzEXUkHAAAArnaEdAAAAMBhCOkAAACAwxDSAQAAAIchpAMAAAAOQ0gHAAAAHIaQDgAAADgMIR0AAABwGEI6AAAA4DCEdAAAAMBhCOkAAACAwxDSAQAAAIchpAMAAAAOQ0gHAAAAHIaQDgAAADgMIR0AAABwGEI6AAAA4DCEdAAAAMBhCOkAAACAwxDSAQAAAIchpAMAAAAOQ0gHAAAAHIaQDgAAADgMIR0AAABwGEI6AAAA4DAlLqQnJyerc+fOmj17dnGXAgAAABSIy8ysuIsoDOnp6YqIiFBaWprCw8OLuxwAAACgwErclXQAAADgakdIBwAAAByGkA4AAAA4DCEdAAAAcBhCOgAAAOAwhHQAAADAYQjpAAAAgMMQ0gEAAACHIaQDAAAADkNIBwAAAByGkA4AAAA4DCEdAAAAcBhCOgAAAOAwhHQAAADAYQjpAAAAgMMQ0gEAAACHIaQDAAAADkNIBwAAAByGkA4AAAA4DCEdAAAAcBhCOgAAAOAwhHQAAADAYQjpAAAAgMMQ0gEAAACHKXEhPTk5WZ07d9bs2bOLuxQAAACgQFxmZsVdRGFIT09XRESE0tLSFB4eXtzlAAAAAAVW4q6kAwAAAFc7QjoAAADgMIR0AAAAwGEI6QAAAIDDENIBAAAAhyGkAwAAAA5DSAcAAAAchpAOAAAAOAwhHQAAAHAYQjoAAADgMIR0AAAAwGEI6QAAAIDDENIBAAAAhyGkAwAAAA5DSAcAAAAchpAOAAAAOAwhHQAAAHAYQjoAAADgMJcd0keMGCGXy+XxExMTUxi1SZI+++wz+fn5qX79+oW2TgAAAMDJ/ApjJTfeeKMWL17svu3r61sYq1VaWpp69Oih1q1ba//+/YWyTgAAAMDpCmW4i5+fn2JiYtw/0dHR7vvOnDmjJ554QnFxcQoJCdEtt9yi5cuX52u9Dz30kO677z41bty4MMoEAAAArgqFEtJ37typ2NhYJSQkKDk5Wd9//737vl69eumzzz7TnDlztHnzZnXp0kXt27fXzp0781znjBkz9N1332n48OGFUSIAAABw1XCZmV3OCv7zn//o5MmTql69uvbv36/Ro0frm2++0bZt23T06FFVq1ZNe/bsUWxsrPsxbdq00c0336yxY8fmuM6dO3eqadOmWrlypapXr64RI0bo/fff18aNG3OtIz09XREREUpLS1N4ePjl7BIAAABQrC57THqHDh3c/69Tp44aN26sqlWr6q233lLFihVlZqpevbrHY06fPq2oqChJUmhoqHt5t27dNHXqVN13330aOXKk1+MAAACAa8FlX0nPyW233abrr79eLVq0UEpKirZt2+b1ZdLQ0FDFxMRo165d7mXh4eEKCAhQmTJlPNpnZmbKzOTr66uFCxeqVatWXtvMvpLeoUMH+fl5fvbo2rWrunbtWsh7CQAAABSNQpnd5XynT5/W119/rWbNmqlBgwY6d+6cDhw4oGbNmuXY/vrrr/e4nZmZqS1btngse/nll7V06VL961//UkJCQp7bnzNnDsNdAAAAcFW77JD+2GOPqVOnTqpUqZIOHDig0aNHKz09XampqapcubJSUlLUo0cPTZw4UQ0aNNChQ4e0dOlS1alTR3/605+81ufj46PatWt7LCtXrpyCgoK8lgMAAAAl0WWH9D179qhr1646dOiQoqOj1ahRI33++eeqXLmypKxZWkaPHq1Bgwbpl19+UVRUlBo3bpxjQAcAAABQRGPSiwOzuwAAAKCkKJR50gEAAAAUHkI6AAAA4DCEdAAAAMBhCOkAAACAwxDSAQAAAIchpAMAAAAOQ0gHAAAAHIaQDgAAADgMIR0AAABwGEI6AAAA4DCEdAAAAMBhCOkAAACAwxDSAQAAAIchpAMAAAAOQ0gHAAAAHIaQDgAAADgMIR0AAABwGEI6AAAA4DCEdAAAAMBhCOkAAACAwxDSAQAAAIcpcSE9OTlZnTt31uzZs4u7FAAAAKBAXGZmxV1EYUhPT1dERITS0tIUHh5e3OUAAAAABVbirqQDAAAAVztCOgAAAOAwhHQAAADAYQjpAAAAgMMQ0gEAAACHIaQDAAAADkNIBwAAAByGkA4AAAA4DCEdAAAAcBhCOgAAAOAwhHQAAADAYQjpAAAAgMMQ0gEAAACHIaQDAAAADkNIBwAAAByGkA4AAAA4DCEdAAAAcBhCOgAAAOAwhHQAAADAYQjpAAAAgMMQ0gEAAACHIaQDAAAADkNIBwAAAByGkA4AAAA4TIkL6cnJyercubNmz55d3KUAAAAABeIyMyvuIgpDenq6IiIilJaWpvDw8OIuBwAAACiwEnclHQAAALjaEdIBAAAAhyGkAwAAAA5DSAcAAAAchpAOAAAAOAwhHQAAAHAYQjoAAADgMIR0AAAAwGEI6QAAAIDDENIBAAAAhyGkAwAAAA5DSAcAAAAchpAOAAAAOAwhHQAAAHAYQjoAAADgMIR0AAAAwGEI6QAAAIDDENIBAAAAhyGkAwAAAA5DSAcAAAAchpAOAAAAOAwhHQAAAHAYQjoAAADgMIR0AAAAwGFKXEhPTk5W586dNXv27OIuBQAAACgQl5lZcRdRGNLT0xUREaG0tDSFh4cXdzkAAABAgZW4K+kAAADA1Y6QDgAAADgMIR0AAABwGEI6AAAA4DCEdAAAAMBhCOkAAACAwxDSAQAAAIchpAMAAAAOQ0gHAAAAHIaQDgAAADgMIR0AAABwGEI6AAAA4DCEdAAAAMBhCOkAAACAwxDSAQAAAIchpAMAAAAOQ0gHAAAAHIaQDgAAADgMIR0AAABwGEI6AAAA4DCEdAAAAMBhCOkAAACAwxDSAQAAAIchpAMAAAAOU+JCenJysjp37qzZs2cXdykAAABAgbjMzIq7iMKQnp6uiIgIpaWlKTw8vLjLAQAAAAqsxF1JBwAAAK52hHQAAADAYQjpAAAAgMMQ0gEAAACHIaQDAAAADkNIBwAAAByGkA4AAAA4DCEdAAAAcBhCOgAAAOAwhHQAAADAYQjpAAAAgMMQ0gEAAACHIaQDAAAADkNIBwAAAByGkA4AAAA4DCEdAAAAyMW5c8WzXUI6AAAAkIPXX5eio6Xjx6/8tgnpAAAAwAV27pQeeUQ6ckTasuXKb5+QjmvC7Nmzi7sEOBD9AjmhXyAn9ItrS0aG1KOHVKGC5OcnbdyYc7ui7BeEdFwTOLkiJ/QL5IR+gZzQL64t48dLX3whzZol1apFSAcAAACK1VdfSSNHSkOGSI0aSfXrS5s2Xfk6COlFwAmftp1Qg+ScOpzAKcfCCXU4oQancMqxcEIdTqjBKZxyLJxQhxNqcAqnHIuSXMfvv0vdu0t160rDhmUtq1dP2rz5ys/yQkgvAk7ovE6oQXJOHU7glGPhhDqcUINTOOVYOKEOJ9TgFE45Fk6owwk1OIVTjkVJrmPIEOn776WZM6WAgKxl9etnhfdduwp9c3nyu7Kbyx8z07Fjxy7pMbt2pUuS9u1LL4qSLklGRobS04uvjsxM6ddfM/T66541mF38sTm1yc+y3Nr88EOGXn45/aLtCqOGvNb1/fcZmjw5/bJquFzffZeh558vvn6RvU+7dmXoueeK93VSGDUUxnO0a1eGJkwo/mNR3DUUVR2X+hzt2pWhv/7VGccipzqK4ryQ27p37szQuHGFcywup+6dOzM0dmzOdVyp4/HttxkaPbrw+kVB6/722ww9+2zedRT1MdmxI0MjRxbv61TKqmPEiIvXUZTHQ8rqn889l67AQCkoKCtUBwZmXfHeu9f7Z98+qVIlqVs36d57pchIz/UtXy69+KI0bpwUHy9lR7nrrsv6d/XqrC+Snq+gmS8sLEwulyvPNi6zoj6Ely49PV0RERHFXQYAAABQ6NLS0hQeHp5nG0eG9IJcSV+0KF13311Ry5f/rAYN8t7pkm7DBqlFC2nRIql2bc/7cvrQlp9lBX1cYa8LAADgfGbSmTPS6dNZ/7pcWVfJc8sRhw5Jc+ZIf/+7tGNH1lXzmBjp22+zrpZXrOj9mC5dskYqvPde4dScnyvpjhzu4nK5Lvrp4kKlS2f9GxAQfsmPLWlCQ7P+LVs2q9MBAAAgS3i49NRTWePP166V/u//pHnzpOnTpRtvzPkxDRtKM2ZkPfZKcWRILwh//6x/z54t3joAAADgfC5X1hSLjRpJr72Wd9v69bPGtR84IJUrd2XqKzGzu2R/A5eQDgAAgMJUr17Wv1dyvvQSF9LPnCneOgAAAFCyVK0qhYQQ0gske7gLIR0AAACFydc36w8cbdx45bZZYkI6w12ubePGjdMf//hHhYWFqVy5crrjjju0Y8cOjzanT59Wv379VLZsWYWEhKhz587as2dPMVWM4jBu3Di5XC49+uij7mX0i2vTL7/8om7duikqKkrBwcGqX7++vvrqK/f9ZqYRI0YoNjZWpUqVUosWLbRt27ZirBhFLSMjQ0OHDlVCQoJKlSql6667TqNGjVJmZqa7Df2i5Pv000/VqVMnxcbGyuVy6f3333ffV6+etHHjxfvAkSNH1L17d0VERCgiIkLdu3fX0aNHL7mWEhfSuZJ+bVqxYoX69Omjzz//XIsWLVJGRobatm2rEydOuNs8+uijmjdvnubMmaNVq1bp+PHjSkpK0rkr/Xd+USzWrVunV199VXXr1vVYTr+49hw5ckSJiYny9/fXf/7zH23fvl0TJ05U6expwiRNmDBBkyZN0pQpU7Ru3TrFxMTotttuu+TpgXH1+Otf/6pXXnlFU6ZM0ddff60JEyboueee00svveRuQ78o+U6cOKF69eppypQpXvfVry9t337xPnDfffdp48aNWrBggRYsWKCNGzeqe/ful16MlRA//5xmkmzGjLTiLqXYffmlmWS2YUNxV1J8Dhw4YJJsxYoVZmZ29OhR8/f3tzlz5rjb/PLLL+bj42MLFiworjJxhRw7dsyqVatmixYtsubNm9sjjzxiZvSLa9XgwYOtadOmud6fmZlpMTExNn78ePeyU6dOWUREhL3yyitXokQUg44dO9r999/vsezOO++0bt26mRn94lokyebNm+e+vXp1pkkx1q9f7n1g+/btJsk+//xzd5s1a9aYJPvmm28uafsl7ko6w10gZf0lL0mK/P9/8/err77S2bNn1bZtW3eb2NhY1a5dW6tXry6WGnHl9OnTRx07dlSbNm08ltMvrk0ffPCBGjZsqC5duqhcuXJq0KCBXjtv/rXdu3dr3759Hv0iMDBQzZs3p1+UYE2bNtWSJUv07bffSpI2bdqkVatW6U9/+pMk+gWksLDdkvapTJnc+8CaNWsUERGhW265xd2mUaNGioiIuOR+UuLmSWe4C8xMAwcOVNOmTVX7///J1X379ikgIEBlypTxaFu+fHnt27evOMrEFTJnzhytX79e69at87qPfnFt+v777zVt2jQNHDhQTz31lL744gv1799fgYGB6tGjh/u5L1++vMfjypcvrx9//LE4SsYVMHjwYKWlpalmzZry9fXVuXPnNGbMGHXt2lWS6BdQenpWH/j559z7wL59+1Quh4nUy5Urd8nvKyUmpPv6Zv1LSEffvn21efNmrVq16qJtzeyif5YXV6+ff/5ZjzzyiBYuXKigoKB8P45+UbJlZmaqYcOGGjt2rCSpQYMG2rZtm6ZNm6YePXq4213YB+gXJds777yjWbNm6R//+IduvPFGbdy4UY8++qhiY2OVmprqbke/wPbtefeBnPpDQfpJiRnuko3hLte2fv366YMPPtCyZcsUHx/vXh4TE6MzZ87oyJEjHu0PHDjgdVUEJcdXX32lAwcO6KabbpKfn5/8/Py0YsUK/e1vf5Ofn5/Kly9Pv7gGVahQQTfccIPHslq1aumnn36SlHW+kOR11Yt+UbI9/vjjevLJJ5WcnKw6deqoe/fuGjBggMaNGyeJfoH/9oFt2/bJ7L/Lz+8DMTEx2r9/v9djDx48eMn9pMSFdK6kX5vMTH379tXcuXO1dOlSJSQkeNx/0003yd/fX4sWLXIv27t3r7Zu3aomTZpc6XJxhbRu3VpbtmzRxo0b3T8NGzZUSkqK+//0i2tPYmKi1xSt3377rSpXrixJSkhIUExMjEe/OHPmjFasWEG/KMFOnjwpHx/PWOTr6+uegpF+gYSEBJUpE6Pjxxcpe4TThX2gcePGSktL0xdffOF+3Nq1a5WWlnbp/aSAX3h1nLS0rNldnnmG2V2uxdldHn74YYuIiLDly5fb3r173T8nT550t/nLX/5i8fHxtnjxYlu/fr21atXK6tWrZxkZGcVYOa6082d3MaNfXIu++OIL8/PzszFjxtjOnTvt7bfftuDgYJs1a5a7zfjx4y0iIsLmzp1rW7Zssa5du1qFChUsPT29GCtHUUpNTbW4uDibP3++7d692+bOnWtly5a1J554wt2GflHyHTt2zDZs2GAbNmwwSTZp0iTbsGGD/fjjj2Zm9tRT402KsMGDc+8D7du3t7p169qaNWtszZo1VqdOHUtKSrrkWkpcSH/ySUL6tRjSJeX4M2PGDHeb33//3fr27WuRkZFWqlQpS0pKsp9++qn4ikaxuDCk0y+uTR9++KHVrl3bAgMDrWbNmvbqq6963J+ZmWnDhw+3mJgYCwwMtFtvvdW2bNlSTNXiSkhPT7dHHnnEKlWqZEFBQXbdddfZ008/badPn3a3oV+UfMuWLcsxT6SmppqZ2blzmVaq1HALDc29Dxw+fNhSUlIsLCzMwsLCLCUlxY4cOXLJtbjMzh9Vc/VKT09XRESEBg5M08SJ4cVdTrH66iupYUNpw4asifcBAABQOG67TQoNlebNK9rtMCYdAAAAyKf69aWNG4t+OyUupDO7CwAAAIpKvXrSDz9IR48W7XZKXEjnSjoAAACKSvZQ4s2bi3Y7JS6kcyUdAAAARaVGDSkgQNq0qWi3U+JCOlfSAQAAUFT8/aXatYt+XHqJC+lcSQcAAEBRql+fK+mXjCvpAAAAKEr16klbt0oZGUW3DUI6AAAAcAnq15dOn5Z27Ci6bZS4kL5+fbI6d+6s2bNnF3cpAAAAKIHq1s36tyjHpfsV3aqLR40ac/TBB9f2XxwFAABA0SldWqpSJSukp6QUzTZK3JV0hrsAAACgqBX1l0dL3JV0ZncBAABAUevbVzp5sujWX+JCOlfSAQAAUNRaty7a9TPcBQAAAHCYEhfSGe4CAACAq12JC+lcSQcAAMDVjpAOAAAAOEyJC+kMdwEAAMDVrsSFdK6kAwAA4GpHSAcAAAAcpsSFdDPp3LnirgIAAAAouBIX0iXGpQMAAODqVjSMzRIAABCxSURBVCJDOkNeAAAAcDUjpAMAAAAOQ0gHAAAAHIaQDgAAADgMIR0AAABwGEI6AAAA4DCEdAAAAMBhCOkAAACAwxDSAQAAAIchpAMAAAAOQ0gHAAAAHIaQDgAAADgMIR0AAABwmBIY0pM1fnxnzZ49u7gLAQAAAArEr7gLKHxz1LdvuLp2Le46AAAAgIIpcVfSXS6GuwD/r737j62rrv84/rpb2yGuXTPm1gYNyCYTAzhmdSJhwjYjOpkl/qCNog5lGv6QxBh/MFDQuEEyTPga4x+EaFBcjYQoiTUkGhaR+IcUNuqvictwmLmMMOxWCK6s/f5x02JZ96NbWc85PB7Jze29vefczw3/PPfm03MBgHKrXKQ3NYl0AADKrZKRPjQ03asAAIATV7lIb2w0SQcAoNwqF+m2uwAAUHYiHQAACqZykW67CwAAZVe5SDdJBwCg7EQ6AAAUTOUi3XYXAADKrnKRbpIOAEDZiXQAACiYykW67S4AAJRd5SLdJB0AgLIT6QAAUDCVi3TbXQAAKLvKRbpJOgAAZVe5SDdJBwCg7CoX6SbpAACUXeUi3SQdAICyq1ykNzUlQ0PTvQoAADhxlYx0k3QAAMqscpFuuwsAAGVXuUg3SQcAoOwqF+k//WlXDhxYk82bN0/3UgAA4IRULtKvu64ntdoD6e7unu6lAADACalcpDc1JYcO1W8AAFBGlYz0xGUYAQAor8pFemNj/d4fjwIAUFaVi/TRSbpIBwCgrEQ6AAAUTOUi3XYXAADKrnKRbpIOAEDZiXQAACiYykW67S4AAJSdSAcAgIKpXKTb7gIAQNlVLtJN0gEAKLvKRfroJH1oaHrXAQAAJ6qykW6SDgBAWVUu0m13AQCg7CoX6SbpAACUnUgHAICCqVykz5yZzJgh0gEAKK/KRXpSn6aLdAAAykqkAwBAwYh0AAAoGJEOAAAFI9IBAKBgRDoAABRM5SK9q6sr//73mvT3b57upQAAwAlpmO4FTLWenp5cfnlL3vzm6V4JAACcmMpN0hPbXQAAKLdKRnpjo0gHAKC8KhnpJukAAJSZSAcAgIKpbKQPDU33KgAA4MRUNtJN0gEAKCuRDgAABSPSAQCgYEQ6AAAUjEgHAICCEekAAFAwIh0AAApGpAMAQMGIdAAAKBiRDgAABSPSAQCgYEQ6AAAUTGUj/dCh+g0AAMrmpCP9M5/5TGq12rjbu9/97qlY25ienp7UarV0dnYe1+ubmur3Q0NTugwAADglGqbiJFdccUV++MMfjj1uGq3kKfDPf/4zX/7yl3PppZce9zGNjfX7gweT006bsqUAAMApMSXbXWbNmpW2trax29y5c8f9fmBgIOvWrcv8+fPT0tKSFStWZNu2bcc876FDh/KJT3wit956a84555zjXs/ovxHsSwcAoIymJNK3bNmS+fPn59xzz811112XvXv3jv1uZGQkq1evzp49e9Lb25u+vr4sXbo0K1euzL59+4563m9961t5wxvekM9+9rOTWo9IBwCgzE56u8sHPvCBfOxjH8tZZ52VnTt35uabb86KFSvS19eXWbNm5aGHHkp/f3/27t2bWbNmJUk2bdqUX/ziF7nvvvuybt26Cc/7yCOP5O67787WrVsnvSZ70gEAKLNJTdLvvffezJ49e+z28MMP5+qrr87q1atz/vnn58orr8yvf/3r/P3vf8+vfvWrJElfX18GBwdzxhlnjDt2586d2bFjR3bt2jXu+Q0bNuTAgQP55Cc/mbvuuivz5s2b9IcySQcAoMwmNUlfs2ZNli1bNvb4zDPPPOw17e3tOeuss/Lkk08mSYaHh9Pe3p4tW7Yc9trW1ta0traOm5bPnTs3O3bsyFNPPZUrr7xy7Pnh4eH6ghsasn379ixcuHDCNXZ1deXAgfrHWrcuaW5Ouru7093dPZmPCgAA02ZSkd7c3Jzm5uajvubZZ5/N008/nfb29iTJ0qVLs2fPnjQ0NOTss8+e8JhFixaNe3z66aenv79/3HM33XRTDhw4kDvvvDNvetObjvj+PT09efLJlnR0JN/9bnLRRcfxwQAAoEBOak/64OBgbrnllnzkIx9Je3t7nnrqqdx4442ZN29errrqqiTJqlWrcvHFF6ezszO33357Fi9enN27d6e3tzednZ3p6Og47LynnXZazj///HHPtba2Jslhz0/EdhcAAMrspCJ95syZ6e/vzz333JP//Oc/aW9vz+WXX56f/exnYxP3Wq2W3t7erF+/Ptdee22eeeaZtLW1Zfny5VmwYMGUfIhXEukAAJRZbWRkZGS6FzEV9u/fnzlz5mRgYCDPPtuSc85JfvObZOXK6V7ZqdfXl3R0JI8/nixZMt2rAQBgsqbkOulFY5IOAECZiXQAACgYkQ4AAAUj0gEAoGBEOgAAFEwlI33mzGTGDJEOAEA5VTLSk/o0XaQDAFBGIh0AAAqmspHe2CjSAQAop8pGukk6AABlJdIBAKBgKh3pQ0PTvQoAAJi8Ske6SToAAGUk0gEAoGBEOgAAFIxIBwCAghHpAABQMCIdAAAKRqQDAEDBiHQAACgYkQ4AAAXTMN0LmGpdXV1paGjI/v3dOXiwe7qXAwAAk1a5SO/p6UlLS0u+8IXk0UenezUAADB5trsAAEDBiHQAACgYkQ4AAAUj0gEAoGAqG+mNjSIdAIByqmykm6QDAFBWlY70oaHpXgUAAExepSPdJB0AgDKqdKS/9FIyPDzdKwEAgMmpdKQntrwAAFA+lY90W14AACgbkQ4AAAUj0gEAoGBEOgAAFIxIBwCAghHpAABQMCIdAAAKRqQDAEDBiHQAACgYkQ4AAAUj0gEAoGBEOgAAFExlI72xsX4v0gEAKJvKRrpJOgAAZdUw3QuYal1dXWloaMjHP96dpDtDQ9O9IgAAmJzKRXpPT09aWloyMpJ86lMm6QA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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "params_values_unbounded = {m:1, s_0:0, s_max:100, t_0:0, r_0:4, th_0:pi/2, ph_0:0, \n", " Dt_0:sqrt(16.405)/2, Dr_0:0.210, Dth_0:0, Dph_0:4.1/16}\n", "\n", "sol_unbounded = geod.solve(step=1, parameters_values=params_values_unbounded, \n", " solution_key='timelike_unbounded_equatorial', verbose=True)\n", "interp_unbounded = geod.interpolate(solution_key='timelike_unbounded_equatorial', \n", " interpolation_key='timelike_unbounded_equatorial', \n", " verbose=True)\n", "\n", "error_squar_norm_unbounded = []\n", "error_e_unbounded = []\n", "error_l_unbounded = []\n", "\n", "i = 0\n", "for (S,T,R,TH,PH) in sol_unbounded:\n", " P = geod(S, interpolation_key='timelike_unbounded_equatorial')\n", " V = geod.tangent_vector_eval_at(S, interpolation_key='timelike_unbounded_equatorial')\n", "\n", " squar_norm_unbounded = numerical_approx((g.at(P)(V,V)).substitute({m:1}))\n", " e_unbounded = numerical_approx((-g.at(P)[0,0]*V[0]).substitute({m:1}))\n", " l_unbounded = numerical_approx((g.at(P)[3,3]*V[3]).substitute({m:1}))\n", " \n", " if i == 0:\n", " squar_norm_unbounded_0 = squar_norm_unbounded\n", " e_unbounded_0 = e_unbounded\n", " l_unbounded_0 = l_unbounded\n", "\n", " error_squar_norm_unbounded += [(S,squar_norm_unbounded - squar_norm_unbounded_0)]\n", " error_e_unbounded += [(S,e_unbounded - e_unbounded_0)]\n", " error_l_unbounded += [(S,l_unbounded - l_unbounded_0)]\n", " \n", " if i == 10:\n", " squar_norm_unbounded_0 = squar_norm_unbounded\n", " e_unbounded_0 = e_unbounded\n", " l_unbounded_0 = l_unbounded\n", "\n", " error_squar_norm_unbounded += [(S,squar_norm_unbounded - squar_norm_unbounded_0)]\n", " error_e_unbounded += [(S,e_unbounded - e_unbounded_0)]\n", " error_l_unbounded += [(S,l_unbounded - l_unbounded_0)] \n", " \n", " i += 1\n", "\n", "plot_error_squar_norm_unbounded = line(error_squar_norm_unbounded)\n", "plot_error_e_unbounded = line(error_e_unbounded)\n", "plot_error_l_unbounded = line(error_l_unbounded)\n", "\n", "plot_error_squar_norm_unbounded.show(title= \n", " \"Timelike geodesic - Unbounded trajectory: error on \" +\n", " \"conservation of squared norm\", \n", " ymin=-1e-3, ymax=1e-3) \n", "plot_error_e_unbounded.show(title=\"Timelike geodesic - Unbounded trajectory: error on conservation of e\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_l_unbounded.show(title=\"Timelike geodesic - Unbounded trajectory: error on conservation of l\",\n", " ymin=-1e-3, ymax=1e-3)\n", "\n", "plot3D_projected_geod_unbounded = geod.plot_integrated(interpolation_key='timelike_unbounded_equatorial',\n", " mapping=BL_spatial_coords, \n", " plot_points=200, thickness=2,\n", " display_tangent=True, \n", " plot_points_tangent=10, scale=8,\n", " width_tangent=1, label_axes=False)\n", "\n", "(plot3D_projected_geod_unbounded + plot3D_event_horizon + plot3D_origin).show(viewer='threejs',\n", " online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Null geodesics\n", "\n", "##### Unstable circular orbit\n", "\n", "The only null, bounded geodesics of Schwarzschild spacetime that do not cross the event horizon induce unstable circular orbits.\n", "In addition, the (constant) radius of such trajectories necessarily equals $3m$.\n", "\n", "Below is provided an example of such a (affinely parametrised) geodesic, for which conservation of squared norm, energy and angular momentum is checked:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing numerical integration with method 'rk4_maxima'...\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_circular_equatorial' (if this key already referred to a former numerical solution, such a solution was erased).\n", "Performing cubic spline interpolation by default...\n", "Interpolation completed and associated with the key 'null_circular_equatorial' (if this key already referred to a former interpolation, such an interpolation was erased).\n" ] }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "params_values_null_circular = {m:1, s_0:0, s_max:60, t_0:0, r_0:3, th_0:pi/2, ph_0:0, \n", " Dt_0:1/sqrt(3), Dr_0:0, Dth_0:0, Dph_0:1/9}\n", "\n", "sol_null_circular = geod.solve(step=1, parameters_values=params_values_null_circular, \n", " solution_key='null_circular_equatorial', verbose=True)\n", "interp_null_circular = geod.interpolate(solution_key='null_circular_equatorial', \n", " interpolation_key='null_circular_equatorial',\n", " verbose=True)\n", "\n", "error_squar_norm_null_circular = []\n", "error_e_null_circular = []\n", "error_l_null_circular = []\n", "error_r_null_circular = []\n", "\n", "i = 0\n", "for (S,T,R,TH,PH) in sol_null_circular:\n", " P = geod(S, interpolation_key='null_circular_equatorial')\n", " V = geod.tangent_vector_eval_at(S, interpolation_key='null_circular_equatorial')\n", " \n", " squar_norm_null_circular = numerical_approx((g.at(P)(V,V)).substitute({m:1}))\n", " e_null_circular = numerical_approx((-g.at(P)[0,0]*V[0]).substitute({m:1}))\n", " l_null_circular = numerical_approx((g.at(P)[3,3]*V[3]).substitute({m:1}))\n", " \n", " if i == 0:\n", " squar_norm_null_circular_0 = squar_norm_null_circular\n", " e_null_circular_0 = e_null_circular\n", " l_null_circular_0 = l_null_circular\n", " R_0 = R\n", "\n", " error_squar_norm_null_circular += [(S, squar_norm_null_circular \n", " - squar_norm_null_circular_0)]\n", " error_e_null_circular += [(S, e_null_circular - e_null_circular_0)]\n", " error_l_null_circular += [(S, l_null_circular - l_null_circular_0)]\n", " error_r_null_circular += [(S, R - R_0)]\n", " \n", " i += 1 \n", "\n", "plot_error_squar_norm_null_circular = line(error_squar_norm_null_circular)\n", "plot_error_e_null_circular = line(error_e_null_circular)\n", "plot_error_l_null_circular = line(error_l_null_circular)\n", "plot_error_r_null_circular = line(error_r_null_circular)\n", "\n", "plot_error_squar_norm_null_circular.show(title=\n", " \"Null geodesic - Circular orbit: error on conservation of squared norm\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_e_null_circular.show(title=\"Null geodesic - Circular orbit: error on conservation of e\", \n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_l_null_circular.show(title=\"Null geodesic - Circular orbit: error on conservation of l\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_r_null_circular.show(title=\"Null geodesic - Circular orbit: error on conservation of r\",\n", " ymin=-1e-3, ymax=1e-3)\n", "\n", "plot3D_projected_geod_null_circular = geod.plot_integrated(interpolation_key='null_circular_equatorial',\n", " mapping=BL_spatial_coords, \n", " plot_points=200, thickness=2,\n", " display_tangent=True, \n", " plot_points_tangent=10, scale=8,\n", " width_tangent=1, label_axes=False)\n", "\n", "(plot3D_projected_geod_null_circular + plot3D_event_horizon + plot3D_origin).show(viewer='threejs',\n", " online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, $g_{\\mu\\nu} \\dot{x}^{\\mu} \\dot{x}^{\\nu}$, $e$ and $l$ are conserved up to negligible numerical variations, the first one being equal to zero as it should.\n", "The fourth graph, which displays the evolution of radial coordinate $r$, confirms that the orbit is circular.\n", "\n", "##### Unbounded trajectory\n", "\n", "Since the type of geodesic considered above is unstable, it is fortunate that numerical roundings do not spoil the numerical integration and allow to visualize the perfectly circular orbit above.\n", "Yet, a tiny variation in the characteristics of the geodesic should significantly change the nature of the trajectory.\n", "For instance, taking an initial radial coordinate $r$ slightly greater than $3m$ induces a diverging trajectory:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing numerical integration with method 'rk4_maxima'...\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_unbounded_equatorial' (if this key already referred to a former numerical solution, such a solution was erased).\n", "Performing cubic spline interpolation by default...\n", "Interpolation completed and associated with the key 'null_unbounded_equatorial' (if this key already referred to a former interpolation, such an interpolation was erased).\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "params_values_null_unbounded = {m:1, s_0:0, s_max:150, t_0:0, r_0:3.01, th_0:pi/2, ph_0:0, \n", " Dt_0:1/sqrt(3.01*1.01), Dr_0:0, Dth_0:0, Dph_0:1/3.01^2}\n", "\n", "sol_null_unbounded = geod.solve(step=1, parameters_values=params_values_null_unbounded, \n", " solution_key='null_unbounded_equatorial', verbose=True)\n", "interp_null_unbounded = geod.interpolate(solution_key='null_unbounded_equatorial', \n", " interpolation_key='null_unbounded_equatorial',\n", " verbose=True)\n", "\n", "error_squar_norm_null_unbounded = []\n", "error_e_null_unbounded = []\n", "error_l_null_unbounded = []\n", " \n", "i = 0\n", "for (S,T,R,TH,PH) in sol_null_unbounded:\n", " P = geod(S, interpolation_key='null_unbounded_equatorial')\n", " V = geod.tangent_vector_eval_at(S, interpolation_key='null_unbounded_equatorial')\n", "\n", " squar_norm_null_unbounded = numerical_approx((g.at(P)(V,V)).substitute({m:1}))\n", " e_null_unbounded = numerical_approx((-g.at(P)[0,0]*V[0]).substitute({m:1}))\n", " l_null_unbounded = numerical_approx((g.at(P)[3,3]*V[3]).substitute({m:1}))\n", " \n", " if i == 0:\n", " squar_norm_null_unbounded_0 = squar_norm_null_unbounded\n", " e_null_unbounded_0 = e_null_unbounded\n", " l_null_unbounded_0 = l_null_unbounded\n", "\n", " error_squar_norm_null_unbounded += [(S, squar_norm_null_unbounded \n", " - squar_norm_null_unbounded_0)]\n", " error_e_null_unbounded += [(S, e_null_unbounded - e_null_unbounded_0)]\n", " error_l_null_unbounded += [(S, l_null_unbounded - l_null_unbounded_0)]\n", " \n", " i += 1\n", "\n", "plot_error_squar_norm_null_unbounded = line(error_squar_norm_null_unbounded)\n", "plot_error_e_null_unbounded = line(error_e_null_unbounded)\n", "plot_error_l_null_unbounded = line(error_l_null_unbounded)\n", "\n", "plot_error_squar_norm_null_unbounded.show(title=\"Null geodesic - Unbounded orbit: error on conservation of \" +\n", " \"squared norm\", ymin=-1e-3, ymax=1e-3)\n", "plot_error_e_null_unbounded.show(title=\"Null geodesic - Unbounded orbit: error on conservation of e\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_l_null_unbounded.show(title=\"Null geodesic - Unbounded trajectory: error on conservation of l\",\n", " ymin=-1e-3, ymax=1e-3)\n", "\n", "plot3D_projected_geod_null_unbounded = geod.plot_integrated(interpolation_key='null_unbounded_equatorial',\n", " mapping=BL_spatial_coords,\n", " plot_points=200, thickness=2,\n", " display_tangent=True,\n", " plot_points_tangent=10, scale=8,\n", " width_tangent=1, label_axes=False)\n", "\n", "(plot3D_projected_geod_null_unbounded + plot3D_event_horizon + plot3D_origin).show(viewer='threejs',\n", " online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An initial radial coordinate a bit smaller than $3m$ would have induced a trajectory plunging into the event horizon.\n", "In order to picture such cases of geodesics crossing the event horizon, switch to ingoing Eddington-Finkelstein coordinates, with respect to which the metric is well-defined even on the event horizon.\n", "\n", "## Geodesics in Eddington-Finkelstein coordinates\n", "\n", "Start with defining the ingoing Eddington-Finkelstein coordinates, set them as the default chart on Schwarzschild spacetime, and provide the transition function from Boyer-Lindquist coordinates to Eddington-Finkelstein coordinates (also ask for the inverse transformation, in order for it to be available to compute the expression of the metric with respect to Edington-Finkelstein frame later):" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & -2 \\, m \\log\\left(\\frac{r}{2 \\, m} - 1\\right) - r + v \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$ " ], "text/plain": [ "t = -2*m*log(1/2*r/m - 1) - r + v\n", "r = r\n", "th = th\n", "ph = ph" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "IEF. = regI_II.chart(r'v r:(0,+oo) th:(0,pi):\\theta ph:\\phi')\n", "Schw.set_default_chart(IEF)\n", "Schw.set_default_frame(IEF.frame())\n", "regI_II.set_default_chart(IEF)\n", "regI_II.set_default_frame(IEF.frame())\n", "\n", "ch_BL_IEF_I = BL_I.transition_map(IEF, [t+r+2*m*ln(r/(2*m)-1), r, th, ph], \n", " restrictions2= r>2*m)\n", "ch_BL_IEF_II = BL_II.transition_map(IEF, [t+r+2*m*ln(1-r/(2*m)), r, th, ph], \n", " restrictions2= r<2*m)\n", "\n", "ch_BL_IEF_I.inverse().display()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} t & = & -2 \\, m \\log\\left(-\\frac{r}{2 \\, m} + 1\\right) - r + v \\\\ r & = & r \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$ " ], "text/plain": [ "t = -2*m*log(-1/2*r/m + 1) - r + v\n", "r = r\n", "th = th\n", "ph = ph" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ch_BL_IEF_II.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metric tensor in the IEF frame\n", "\n", "From the transition map `ch_BL_IEF_I` defined above, Sage can compute the components of the metric tensor in the IEF frame in region $\\mathcal{R}_{\\mathrm{I}}$:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "IEF_I = IEF.restrict(regI)\n", "IEF_II = IEF.restrict(regII)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{2 \\, m - r}{r} \\right) \\mathrm{d} v\\otimes \\mathrm{d} v +\\mathrm{d} v\\otimes \\mathrm{d} r +\\mathrm{d} r\\otimes \\mathrm{d} v + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "g = (2*m - r)/r dv*dv + dv*dr + dr*dv + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(IEF_I.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We extend these components to all the IEF domain by analytic continuation:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "g.add_comp_by_continuation(IEF.frame(), regI, IEF)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the IEF frame is now the default frame, we have then" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{2 \\, m - r}{r} \\right) \\mathrm{d} v\\otimes \\mathrm{d} v +\\mathrm{d} v\\otimes \\mathrm{d} r +\\mathrm{d} r\\otimes \\mathrm{d} v + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "g = (2*m - r)/r dv*dv + dv*dr + dr*dv + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The initial conditions are stored in the tangent vector `v_0`, whose components `(Dt_0, Dr_0, Dth_0, Dph_0)` were set in terms of the coordinate frame associated with Boyer-Lindquist coordinates. To get them in terms of the IEF frame, we have to add manually \n", "the tangent space automorphism linking the BL basis to the the IEF one in the tangent tangent space $\\mathcal{T}_{p_{0}}\\mathcal{Schw}$ (this is because the point $p_0$ has been declared before the transition map `ch_BL_IEF_I`; otherwise the tangent space automorphism would have been automatically computed from the change of coordinate frames induced by `ch_BL_IEF_I`)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent space at Point p_0 on the 4-dimensional Lorentzian manifold Schw\n" ] } ], "source": [ "T_0 = v_0.parent()\n", "print(T_0)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "T_0.set_change_of_basis(BL_I.frame().at(p_0), IEF.frame().at(p_0),\n", " Schw.change_of_frame(BL_I.frame(), IEF_I.frame()).at(p_0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The components of `v_0` with respect to the tangent space basis induced by the IEF frame can\n", "then be computed:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\mathit{Dt}_{0} - \\frac{\\mathit{Dr}_{0} r_{0}}{2 \\, m - r_{0}}, \\mathit{Dr}_{0}, \\mathit{Dth}_{0}, \\mathit{Dph}_{0}\\right]$ " ], "text/plain": [ "[Dt_0 - Dr_0*r_0/(2*m - r_0), Dr_0, Dth_0, Dph_0]" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v_0[IEF.frame().at(p_0),:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One may now declare a new parametrised geodesic set in terms of Eddington-Finkelstein coordinates:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "scrolled": 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, Dr_0, Dt_0, Dth_0, m, ph_0, r_0, s_0, s_max, t_0, th_0].\n" ] } ], "source": [ "geod_IEF = Schw.integrated_geodesic(g, affine_param, v_0, verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From an abstract point of view, it is the same as the geodesic `geod` previously used, but the equations defining it are now expressed in terms of Eddington-Finkelstein coordinates, so that the numerical solutions computed will correspond to Eddington-Finkelstein coordinates as well.\n", "Check this by displaying the system defining it:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Geodesic in the 4-dimensional Lorentzian manifold Schw equipped with Lorentzian metric g on the 4-dimensional Lorentzian manifold Schw, and integrated over the Real interval (s_0, s_max) as a solution to the following geodesic equations, written with respect to Chart (R_I_union_R_II, (v, r, th, ph)):\n", "\n", "Initial point: Point p_0 on the 4-dimensional Lorentzian manifold Schw with coordinates [-2*m*log(2) - 2*m*log(m) + 2*m*log(-2*m + r_0) + r_0 + t_0, r_0, th_0, ph_0] with respect to Chart (R_I_union_R_II, (v, r, th, ph))\n", "Initial tangent vector: Tangent vector at Point p_0 on the 4-dimensional Lorentzian manifold Schw with components [Dt_0 - Dr_0*r_0/(2*m - r_0), Dr_0, Dth_0, Dph_0] with respect to Chart (R_I_union_R_II, (v, r, th, ph))\n", "\n", "d(v)/ds = Dv\n", "d(r)/ds = Dr\n", "d(th)/ds = Dth\n", "d(ph)/ds = Dph\n", "d(Dv)/ds = (Dph^2*r^3*sin(th)^2 + Dth^2*r^3 - Dv^2*m)/r^2\n", "d(Dr)/ds = -(2*Dth^2*m*r^3 - Dth^2*r^4 - 2*Dv^2*m^2 - (2*Dr*Dv - Dv^2)*m*r + (2*Dph^2*m*r^3 - Dph^2*r^4)*sin(th)^2)/r^3\n", "d(Dth)/ds = (Dph^2*r*cos(th)*sin(th) - 2*Dr*Dth)/r\n", "d(Dph)/ds = -2*(Dph*Dth*r*cos(th) + Dph*Dr*sin(th))/(r*sin(th))\n", "\n" ] } ], "source": [ "sys = geod_IEF.system(verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Timelike plunging geodesic\n", "\n", "The following example defines a timelike geodesic (parametrised with proper time) with same angular momentum as that of timelike geodesics previously considered, which crosses the event horizon $\\mathcal{H}$.\n", "Notice that, in Eddington-Finkelstein coordinates, energy $e$ per unit mass is computed from the following relation:\n", "\n", "$$e = \\left( 1 - \\frac{2m}{r} \\right) \\dot{v} - \\dot{r}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Provide the parameters values, integrate and interpolate:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing numerical integration with method 'rk4_maxima'...\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_plunging_equatorial' (if this key already referred to a former numerical solution, such a solution was erased).\n", "Performing cubic spline interpolation by default...\n", "Interpolation completed and associated with the key 'timelike_plunging_equatorial' (if this key already referred to a former interpolation, such an interpolation was erased).\n" ] } ], "source": [ "params_values_plunging = {m:1, s_0:0, s_max:15, t_0:0, r_0:3.8, th_0:pi/2, ph_0:0, \n", " Dt_0:sqrt(31.25/(3.8*1.8)), Dr_0:0, Dth_0:0, Dph_0:4.1/(3.8)^2}\n", "\n", "sol_plunging = geod_IEF.solve(step=0.1, parameters_values=params_values_plunging, \n", " solution_key='timelike_plunging_equatorial', verbose=True)\n", "interp_plunging = geod_IEF.interpolate(solution_key='timelike_plunging_equatorial', \n", " interpolation_key='timelike_plunging_equatorial',\n", " verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check conservation of norm, energy and angular momentum:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "error_squar_norm_plunging = []\n", "error_e_plunging = []\n", "error_l_plunging = []\n", "\n", "i = 0\n", "for (S,T,R,TH,PH) in sol_plunging: \n", " P = geod_IEF(S, interpolation_key='timelike_plunging_equatorial')\n", " V = geod_IEF.tangent_vector_eval_at(S, interpolation_key='timelike_plunging_equatorial') \n", " # print(i)\n", " squar_norm_plunging = numerical_approx((g.at(P)(V,V)).substitute({m:1}))\n", " e_plunging = numerical_approx((-g.at(P)[0,0]*V[0] - V[1]).substitute({m:1}))\n", " l_plunging = numerical_approx((g.at(P)[3,3]*V[3]).substitute({m:1}))\n", " \n", " if i == 0:\n", " squar_norm_plunging_0 = squar_norm_plunging\n", " e_plunging_0 = e_plunging\n", " l_plunging_0 = l_plunging\n", " \n", " if i == 10:\n", " squar_norm_plunging_0 = squar_norm_plunging\n", " e_plunging_0 = e_plunging\n", " l_plunging_0 = l_plunging \n", " \n", " error_squar_norm_plunging += [(S,squar_norm_plunging - squar_norm_plunging_0)]\n", " error_e_plunging += [(S,e_plunging - e_plunging_0)]\n", " error_l_plunging += [(S,l_plunging - l_plunging_0)]\n", " \n", " i += 1\n", " \n", "plot_error_squar_norm_plunging = line(error_squar_norm_plunging)\n", "plot_error_e_plunging = line(error_e_plunging)\n", "plot_error_l_plunging = line(error_l_plunging)\n", "\n", "plot_error_squar_norm_plunging.show(title=\"Timelike geodesic - Plunging trajectory: error on conservation of \" + \n", " \"squared norm\", ymin=-1e-3, ymax=1e-3)\n", "plot_error_e_plunging.show(title=\"Timelike geodesic - Plunging trajectory: error on conservation of e\",\n", " ymin=-1e-1, ymax=1e-1)\n", "plot_error_l_plunging.show(title=\"Timelike geodesic - Plunging trajectory: error on conservation of l\",\n", " ymin=-1e-3, ymax=1e-3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to plot the spatial part of the geodesic, define the mapping converting the spatial part of Eddingon-Finkelstein coordinates (i.e. the polar coordinates) into the Cartesian coordinates; this mapping obviously has the same form as that previously used on the Boyer-Lindquist coordinates: " ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "IEF_spatial_coords = Schw.diff_map(R3, {(IEF, cart): [r*sin(th)*cos(ph), r*sin(th)*sin(ph),\n", " r*cos(th)]})" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "This finally allows to plot the spatial part of the geodesic:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot3D_projected_geod_IEF_plunging = geod_IEF.plot_integrated(interpolation_key='timelike_plunging_equatorial',\n", " mapping=IEF_spatial_coords,\n", " plot_points=200, thickness=2,\n", " display_tangent=True,\n", " plot_points_tangent=10,\n", " scale=0.5,\n", " width_tangent=1,\n", " label_axes=False)\n", "\n", "(plot3D_projected_geod_IEF_plunging + plot3D_event_horizon + plot3D_origin).show(viewer='threejs',\n", " online=True)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "##### Null plunging geodesic\n", "\n", "The following example defines a (affinely parametrised) null geodesic with same angular momentum as that of nulll geodesics previously considered, which crosses the event horizon $\\mathcal{H}$ due to an initial radial coordinate $r$ slightly smaller than $3m$." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Performing numerical integration with method 'rk4_maxima'...\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_plunging_equatorial' (if this key already referred to a former numerical solution, such a solution was erased).\n", "Performing cubic spline interpolation by default...\n", "Interpolation completed and associated with the key 'null_plunging_equatorial' (if this key already referred to a former interpolation, such an interpolation was erased).\n" ] } ], "source": [ "params_values_null_plunging = {m:1, s_0:0, s_max:43.9, t_0:0, r_0:2.99, th_0:pi/2, ph_0:0, \n", " Dt_0:1/sqrt(2.99*0.99), Dr_0:0, Dth_0:0, Dph_0:1/(2.99)^2}\n", "\n", "sol_null_plunging = geod_IEF.solve(step=0.1, parameters_values=params_values_null_plunging, \n", " solution_key='null_plunging_equatorial', verbose=True)\n", "interp_null_plunging = geod_IEF.interpolate(solution_key='null_plunging_equatorial', \n", " interpolation_key='null_plunging_equatorial',\n", " verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check conservation of norm, energy and angular momentum, and display the spatial part of the geodesic:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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K0oMPPqj8/Hx99913xba3ZMkS2Ww29e3b1+3YxsbGKiUlxXWef/HFF8rJydHjjz8um8123XGX9H1itZ0BAQEaNmyYlixZov3790uS9uzZo2XLlnnENW/ePOXl5SkhIcEyriVLligqKkp33nmn2/a3aNFC0dHRHtPJmjVrVmxdSNeuXRUZGemx3Q6HQ3fffbfb8sL9cPV2F9VGUYrbn23atFH9+vU92k1ISHC7GILNZlNycnKRV7a70meffSZJGjp0qFdj+dWvfqUtW7Zo2LBhWr58uXJyctzaOHfunNasWaN77rlHoaGhbsfuzjvv1Pnz5z2mft5zzz0esfft21d2u91titL8+fN18eJFDRw40LXs0qVLmjRpkho3bqzg4GDZ7XYFBwdr7969+ve//13svrHirWNYXD/p6ekKCQnx6AcoDkkDvCY9PV233XabnnvuOY951t5y6tQpSVJMTIzHc1cvO3bsmLZv3+76wFv4ExERIWOM6wP6qVOnZLfbPQpnbTabYmNjXX0W/o6NjXVbz263KyoqyqPvxYsXe/R96623SpKr7379+mn27Nn68ccfdc8996hGjRpq1aqVVqxYUew+KKwj+DkFeUlJSW7xTJw4sUSv2bRpkzZv3qydO3cqKytL77//fok+GF2Pq/dhpUqVJF2eyyv99zhVq1bNbb2izoWS9lHYT2Efhf2U5Pz6uYq6otP+/fvVrl07HTp0SDNmzNC6deu0adMmV33BlfFd7dixYzLGKCYmxuN827hxo+tcu5HzRir5+8RqOyXpoYceUmhoqGbNmiXpci1HaGioHnrooZ8V17Fjx3Tq1CmPbQ8KCtLJkyc9EnGrK2oV9dypU6eKXB4bGyubzVbi7S6q3eLWj4+P92i3JOduUU6cOKHg4GDLCwOURSxjx47V1KlT9fnnn6tHjx6KiopS165d9fXXX0u6/DcwPz9fr776qsdxK/wCoSTHrnr16urVq5fmzZvn+hJk7ty5atOmjRo2bOha78knn9T48eP129/+VkuWLNGXX36pTZs26dZbb73mPiyOt47hqVOnVKlSJVWtWtVteUBAgGJiYjz6AYrD1ZPgNTabTS+//LK6deumv/3tbx7PF37rnZub67a8NP+gFf7RPXbsmMdzR48edRttiI6OVmhoqGbPnl1kW9HR0a428/LydOLECbf/WI0xOnr0qH75y1+69X306FG3bz/z8vI8tjE6OlpNmzbViy++WGTf8fHxrn8PHDhQAwcO1Llz5/TPf/5T48aNU69evfTdd98pMTHR47WFMR48eLDItq0sXrzY7fhcGUdxCovNr0dZnAuFx+mnn35ySxyOHj36s9ssrp/izq/SUNS3/J988onOnTunjz/+2O2Yb9u27ZrtRUdHy2azad26da5E60qFy27kvJFK/j4pVNxoRmRkpPr376+3335bo0eP1pw5c/TAAw+oSpUqPyuu6OhoxcTEaMmSJUU+73A4ShRXcc9FRUUVeRyOHj0qY4zr70hJ2r+6XUk6cuSIxxcRhw8fLrUktXr16rp48aLHcSvrWIKCgjR69GiNHj1ap0+f1sqVKzVmzBh1795dBw4cULVq1RQQEKCBAwfq0UcfLbKNunXruj0ubt8OHDhQCxcu1KpVq1SjRg1t3brVYyT0/fff18CBA11FzYVOnjzpsc0l5a1jGBUVpdzcXJ0+fdotcSgoKNCxY8fUrl27UukHFR8jDfCqrl27qlu3bpo4caLOnj3r9lxMTIxCQkI8rm+9aNGiUuu/VatWqlSpkj744AO35Rs3bvQY4u3Vq5f27NmjqKgotWzZ0uOnMMHo0qWLJHlcZeKjjz7SuXPnXM8XXplp/vz5but9+OGHHldE6tWrl3bu3KmkpKQi+y7qw3p4eLhSU1P13HPP6eLFi25X9bhSgwYNlJSUpNmzZ3t8KL+W5OTka8ZRGsriXOjQoYMkeRx7p9P5s9ssrp+dO3fqX//618/q5+oRkpIo/DB05Yd+Y0yJpoD16tVLxhgdOnSoyHMtOTlZ0uUpE5GRkZo1a5bl1VqKi7+k75OSeOKJJ3Ty5Ende++9ysrK0rBhw0r82qv16tVLx44dk81mK3L7i5oKdj26dOmi7OxsLV682G35u+++63r+5+jcubMkz/25ceNG7d69+2e3e7XCKZFXX5HIm7FUrVpV9913nx577DGdPHlS+/fvV0REhNq3b6+tW7cqJSWlyGN39ahicVJTUxUbG6s5c+Zozpw5CgsL0+9+9zu3dWw2m0dSvWjRIo8vCK7n/eutY1jce+/DDz/UhQsXSq0fVHyMNMDrXn75ZbVo0ULHjx93TbeR5JpXPXv2bCUlJSklJUVfffWVFixYUGp9V6tWTU899ZSmTJmiqlWr6u6773bdjKfwDpiFRowYoY8++kjt27fXyJEj1bRpUxUUFGj//v1avny5Ro0apVatWqlbt27q3r27nn32WeXk5Kht27bavn27xo0bp+bNm6tfv36SpF/84hfq27ev/vznPysoKEhdu3bVzp079corr3h8mzlx4kStWLFCbdq00RNPPKGGDRvqwoUL2rdvn5YuXapZs2apZs2aeuSRRxQaGqq2bdsqLi5OR48e1ZQpUxQZGenxze2V3njjDfXu3Vu33367Ro4cqVq1amn//v36v//7P4+kxhfK4lzo0aOH2rZtq1GjRiknJ0ctWrTQhg0bXB/erjz2N2LEiBGaPXu2UlNTNXHiRMXExGjBggX6f//v/5Won8IP6TNmzFD//v0VFBSkhg0bKiIiotjXdOvWTcHBwcrIyNAzzzyjCxcuaObMmTp9+vQ1423btq0GDx6sgQMHavPmzWrfvr3Cw8N15MgRff7550pOTtZjjz2mypUra9q0aXr44YfVtWtXPfLII4qJidH333+vb775xnUpzML4X375ZaWmpiowMFBNmzYt8fukJBo0aKAePXros88+0x133FHk/V/69++v+fPn68cff7Ssa+jTp48WLFig7t27a8SIEWrZsqXsdrsOHTqkVatW6d5771Xv3r1LHNvVBgwYoJkzZ6pv376aOHGiGjdurHXr1mnKlClKS0vzuMxzSd1666166KGH9Oqrr0qSunfvrr179+r5559XYmKinnjiiZ8d85U6deqkjIwMjR8/XkeOHFHPnj0VFBSkrVu3KiIiQkOHDi2TWO688041a9ZMLVq0UPXq1bV371699tprqlu3rmsE4S9/+YvatWun9u3b69FHH1Xt2rWVk5Oj3bt369NPPy3xXH273a5+/frptddeU+XKlXXvvfd6vN969eqld955R/Xr11dycrI2bdqkadOmeZxb9evXV0hIiN577z01aNBA4eHhSkhIKHIKkreOYWpqqrp27arRo0crKytLrVu31jfffKNx48apZcuWeuCBB0qlH9wEfFeDjYruyqsnXe2BBx4wkjwux5mdnW0efvhhExMTY8LDw03v3r3Nvn37SvWSqwUFBWbSpEmmZs2aJjg42DRt2tQsWbLEpKSkmLvvvttt3bNnz5qxY8eahg0bmuDgYBMZGWmSk5PNyJEj3S5Fef78efPss8+axMREExQUZOLi4sxjjz1mTp8+7dZebm6uGTVqlKlRo4YJCQkxt99+u9mwYYNJTEx0u3qSMcacOHHCPPHEE6ZOnTomKCjIVKtWzbRo0cI899xz5uzZs8YYY+bNm2c6depkYmJiTHBwsImPjzf333+/2b59u6udoq6eZMzlq3ykpqaayMhIU6lSJZOUlORxZacbVdwlV69W1LEr6blQePWkqy8NWNQ58tNPP5mBAweaKlWqmLCwMNOtWzfXVXJmzJhh+dritqWo2Hfu3Gm6du1qQkJCTLVq1cygQYPMvHnzjCTzzTffXHN/jBkzxsTHx5uAgAC3Y5eYmFjslVIWL15sUlJSTEhIiElISDBPP/20+eyzzzyOff/+/U3t2rU9Xj979mzTqlUrEx4ebkJDQ01SUpJ58MEHzebNm93WW7p0qenQoYMJDw83YWFhpnHjxubll192PZ+bm2sefvhhU716dWOz2dz2Y0nfJ1bbWWju3LlGknE6nUU+X9JLrhpjzMWLF83UqVNN06ZNTUhIiKlcubJp1KiRefTRR92uqpOQkOBx5SZj/nvloyeffLLI9k+ePGkGDx5sYmNjjd1uN7Vr1zbPPfec61KXJWmjKHl5eWby5Mmmfv36JigoyERHR5t+/fqZQ4cOua3Xtm1bk5KS4vH6kl79Jj8/30ybNs3ceuutJjg42FSpUsW0adPGdQW5sohl6tSppk2bNiY6OtoEBwebWrVqmUceecTs37/f7XV79uwxAwYMcF3Zqnr16qZt27ZmypQprnUKr560cOHCYrfxX//6l5FU7BXOCv92VK9e3YSFhZl27dqZ9evXm7Zt25ouXbq4rfv++++bhg0bmqCgICPJvPDCC8aYoi+56q1jeO7cOfP000+bWrVqmaCgIBMfH2+GDh3qcaUurp4EKzZjSnBXEKCC27t3rxo1aqRx48a53RgNFd+CBQvUp08frV+/Xm3atCmzfgYPHqzMzEydOnVKwcHBZdbPtdx99906cOCANm/e7LMYSsM999yjjRs3at++feXyruIAUNEwPQk3nW+++UaZmZlq06aNHA6Hvv32W02dOlUOh0ODBg3ydXgoQ5mZmTp06JCSk5MVEBCgjRs36k9/+pPat29fqgnDxIkTFR8fr7p16+rs2bNasmSJ3n77bY0dO9ZnCcP+/fv1xRdfaPXq1dc1Fag8yc3N1ddff62vvvpKCxcu1PTp00kYAMBLSBpw0wkPD9fmzZv1zjvvKCsrS5GRkerYsaNefPHFUrtaBcqniIgIOZ1OTZo0SefOnVNcXJwGDBjgcUWUGxUUFKQ//elPOnjwoPLy8lS/fn1Nnz5dTz75ZKn2cz1mz56tP//5z+rcubPGjRvnszhuxJEjR1zJ/pAhQzR8+HBfhwQANw2mJwEAAACwxCVXAQAAAFgiaQAAAABgqcIkDcYY5eTkWN50CAAAAMD1qzBJw5kzZxQZGakzZ874OhQAAACgzC1eLNlsUtu2Zd9XhUkaAAAAgJtJ4QQbm63s+yJpAAAAAPwQSQMAAAAAS36VNPzzn/9U7969FR8fL5vNpk8++eSGg/r888/Vtm1bRUVFKTQ0VI0aNdKrr756w+0CAAAAuH43fEfoc+fOKSUlRQMHDtQ999xTGjEpPDxcw4YNU9OmTRUeHq7PP/9cQ4YMUXh4uAYPHlwqfQAAAAD+zJsXDb3hpCE1NVWpqanFPn/x4kWNHTtW8+fPV1ZWlpo0aaKXX35ZHTt2LPY1zZs3V/PmzV2Pa9eurY8//ljr1q0jaQAAAADkZ9OTrmXgwIFav369nE6ntm/frvvuu089evTQ7t27S9zG1q1b9cUXX6hDhw5lGCkAAADgP7yZNNzwSIOVPXv2KDMzUwcPHlR8fLwkafTo0Vq2bJnmzJmjyZMnW76+Zs2aOnHihPLy8jR+/Hg9/PDDZRkuAAAA4Hf8Pmn4+uuvZYxRgwYN3Jbn5uYqKipKklS5cmXX8r59+2rWrFmux+vWrdPZs2e1ceNG/f73v1e9evWUkZFRliEDAAAAfsGvahqsFBQUKDAwUFu2bFFgYKDbc4XJwrZt21zLHA6H2zp16tSRJCUnJ+vYsWMaP378NZOG9PR02e3um5WRkUGyAQAAgAqlwiQNzZs3V35+vo4fP6527doVuU69evVK1JYxRrm5uddcz+l0eiQfAAAAQEXjVzUNZ8+e1ffff+96vHfvXm3btk3VqlVTgwYN1KdPHz344IOaNm2amjdvrpMnT2rVqlVKTk7WnXfeWWSbb7zxhmrVqqVGjRpJunzfhldeeUXDhw+/0XABAACACsUvkobNmzerU6dOrsdPPfWUJKl///6aO3eu5syZo0mTJmnUqFE6dOiQoqKi1Lp162ITBunytKYxY8Zo7969stvtSkpK0ksvvaQhQ4bcaLgAAABAheDN6Uk2Y7zZXdnJyclRZGSksrOzmZ4EAACACs/plDIypC5dpJUry7avMr9PAwAAAIDS582v/kkaAAAAAD9WIe4IDQAAAKD0MdIAAAAAwJI3L7lK0gAAAAD4IZKHcst0AAAgAElEQVQGAAAAAOUGSQMAAADgh6hpAAAAAGCJ6UkAAAAALJE0AAAAACgRkgYAAAAARaKmAQAAAIAlkgYAAAAAlqhpAAAAAGCJpAEAAABAuUHSAAAAAPghahoAAAAAWGJ6EgAAAABLjDQAAAAAKBFvJA8kDQAAAIAfYqQBAAAAgCWShhuQnp6utLQ0ZWZm+joUAAAAoMx4M2mwe68r73A6nXI4HL4OAwAAAKgwKtxIAwAAAHAzKBxpoBAaAAAAQJGoaQAAAABgiaQBAAAAQLlB0gAAAAD4IUYaAAAAAFiiEBoAAACAJUYaAAAAAJQbJA0AAACAH2KkAQAAAIAlkgYAAAAAliiEBgAAAFBukDQAAAAAfojpSQAAAAAskTQAAAAAsETSAAAAAKBEKIQGAAAAUCRGGgAAAABYImkAAAAAYImkAQAAAIAlkgYAAAAAJUIhNAAAAIAiMdIAAAAAwBJJAwAAAABLJA03ID09XWlpacrMzPR1KAAAAECFYPd1AKXN6XTK4XD4OgwAAACgTBWONFAIDQAAAKBITE8CAAAAYImkAQAAAEC5QdIAAAAA+CFqGgAAAABYYnoSAAAAAEskDQAAAADKDZIGAAAAwA8x0gAAAADAEoXQAAAAACwx0gAAAACg3CBpAAAAAPwQIw0AAAAALJE0AAAAALBEITQAAACAcoOkAQAAAPBDTE8CAAAAYImkAQAAAIAlkgYAAAAAJUIhNAAAAIAiMdIAAAAAwBJJAwAAAABLJA0AAAAALJE0AAAAACgRCqEBAAAAFImRhhuQnp6utLQ0ZWZm+joUAAAAoMx4M2mwe68r73A6nXI4HL4OAwAAAChTjDQAAAAAKDdIGgAAAAA/VDjSQCE0AAAAgCIxPQkAAACAJZIGAAAAAOUGSQMAAADgh6hpAAAAAGCJ6UkAAAAALJE0AAAAACg3SBoAAAAAP8RIAwAAAABLFEIDAAAAsMRIAwAAAIByg6QBAAAA8EOMNAAAAACwRNIAAAAAwBKF0AAAAADKDZIGAAAAwA8xPQkAAACAJZIGAAAAAJZIGgAAAABYohAaAAAAQLlB0gAAAAD4IaYnAQAAALBE0nAD0tPTlZaWpszMTF+HAgAAAJQZbyYNdu915R1Op1MOh8PXYQAAAABeQSE0AAAAgCIxPQkAAACAJZIGAAAAAJZIGgAAAACUGyQNAAAAgB/ijtAAAAAALDE9CQAAAIAlkgYAAAAA5QZJAwAAAOCHGGkAAAAAYIlCaAAAAACWGGkAAAAAUG6QNAAAAAB+iJEGAAAAAJaoaQAAAABgiZEGAAAAAOUGSQMAAADghxhpAAAAAGDJr5KG8ePHy2azuf3ExsaWRmySpPXr18tut6tZs2al1iYAAADg77xZCG0vjUZuvfVWrVy50vU4MDCwNJpVdna2HnzwQXXp0kXHjh0rlTYBAAAAXJ9SmZ5kt9sVGxvr+qlevbrruYsXL+qZZ55RQkKCwsPD1apVK61Zs6ZE7Q4ZMkQPPPCAWrduXRphAgAAABWGX01PkqTdu3crPj5ederUUXp6un744QfXcwMHDtT69evldDq1fft23XffferRo4d2795t2eacOXO0Z88ejRs3rjRCBAAAACoUbyYNNzw9qVWrVnr33XfVoEEDHTt2TJMmTVKbNm20a9cuZWVlKTMzUwcPHlR8fLwkafTo0Vq2bJnmzJmjyZMnF9nm7t279fvf/17r1q2T3V4qM6gAAACACsWvkobU1FTXv5OTk9W6dWslJSVp3rx5uuWWW2SMUYMGDdxek5ubq6ioKElS5cqVXcv79u2rN954Qw888IAmTJjg8ToAAAAAl/ldIfSVwsPDlZycrN27dyshIUGBgYHasmWLR3F0YbKwbds21zKHw6EzZ85o8+bN2rp1q4YNGyZJKigokDFGdrtdy5cvV+fOnYvtPz093WN0IiMjQxkZGaW1iQAAAMBNpdSThtzcXP373/9Wu3bt1Lx5c+Xn5+v48eNq165dkevXq1fP7XFBQYF27NjhtuzNN9/UqlWr9Pe//1116tSx7N/pdMrhcNzYRgAAAADlnF9NTxo9erR69+6tWrVq6fjx45o0aZJycnLUv39/JSYmqk+fPnrwwQc1bdo0NW/eXCdPntSqVauUnJysO++806O9gIAANWnSxG1ZjRo1FBIS4rEcAAAAuFn5VdJw8OBBZWRk6OTJk6pevbpuv/12bdy4UYmJiZIuXwVp0qRJGjVqlA4dOqSoqCi1bt26yIQBAAAAQMl4M2mwGePN7spOTk6OIiMjlZ2dzfQkAAAAVHjdukkrV0otW0qbNpVtX6VynwYAAAAA3uV3N3cDAAAA4F0kDQAAAAAskTQAAAAAKDdIGgAAAAA/5M07QpM0AAAAAH6I6UkAAAAALJE0AAAAACg3SBoAAAAAP8RIAwAAAABLFEIDAAAAsMRIAwAAAIByg6QBAAAA8EOMNAAAAACwRE0DAAAAAEuMNAAAAAAoN0gaAAAAAD/ESAMAAAAASyQNAAAAACxRCA0AAACg3CBpAAAAAPwQ05NuQHp6utLS0pSZmenrUAAAAIAy482kwe69rrzD6XTK4XD4OgwAAACgTDHSAAAAAMAShdAAAAAAyg2SBgAAAMAPMT0JAAAAgCWSBgAAAACWSBoAAAAAlAiF0AAAAACKxEgDAAAAAEskDQAAAAAskTQAAAAAKDdIGgAAAAA/xB2hAQAAAFhiehIAAAAASyQNAAAAAMoNkgYAAADADzHSAAAAAMAShdAAAAAALDHSAAAAAKDcIGkAAAAA/BAjDQAAAAAskTQAAAAAsEQhNAAAAIByg6QBAAAA8ENMTwIAAABgiaThBqSnpystLU2ZmZm+DgUAAAAoM96sabCXfRfe5XQ65XA4fB0GAAAAUKYYaQAAAABQbpA0AAAAAH6IkQYAAAAAlkgaAAAAAFji5m4AAAAAyg2SBgAAAMAPMT0JAAAAgCWSBgAAAACWSBoAAAAAlAiF0AAAAACKxEgDAAAAAEskDQAAAAAskTQAAAAAKDdIGgAAAAA/xB2hAQAAAFhiehIAAAAASyQNAAAAAMoNkgYAAADADzHSAAAAAMAShdAAAAAALDHSAAAAAKDcIGkAAAAA/JAxUoCXPs2TNAAAAAB+yBjJZvNOXyQNAAAAgB+iEPoGpKenKy0tTZmZmb4OBQAAAChT3hppsHunG+9xOp1yOBy+DgMAAAAoU0xPAgAAAGCJQmgAAAAAlhhpAAAAAGCJQmgAAAAA18RIAwAAAIBiUdMAAAAAwBI1DQAAAAAsUdMAAAAA4JoYaQAAAABQLKYnAQAAALBE0gAAAADAEkkDAAAAgGuy2SiEBgAAAFAMRhoAAAAAWCJpAAAAAHBNJA0AAAAALJE0AAAAAChSYfEzhdAAAAAAinRl0uANJA0AAACAn8jNlerVk776yrv9kjQAAAAAfiIrS9qzR/rhh8uPA7z0aZ6kAQAAAPAT585d/p2ff/k305MAAAAAuPnPfy7/zsu7/JtCaAAAAABurk4avIWkAQAAAPAThUkD05NuUHp6utLS0pSZmenrUAAAAIBSdXXS4K1CaLt3uvEep9Mph8Ph6zAAAACAUldYCH1lTYM3VLiRBgAAAKCiohAaAAAAgCUKoQEAAABY8lVNA0kDAAAA4Ce4uRsAAAAAS0XVNHgDSQMAAADgJ4qqaaAQGgAAAIALIw0AAAAALFEIDQAAAMAShdAAAAAALFHTAAAAAMASNQ0AAAAALF1d00DSAAAAAMBNYU0DIw0AAAAAisRIAwAAAABLRdU0UAgNAAAAwIWRBgAAAADFys+XcnMv/5uaBgAAAAAeCkcZJJIGwK9lZmb6OgTc5DgH4Wucg/C1inwOXpk0MD0J8GMV+Q8V/APnIHyNcxC+VpHPweKSBgqhAQAAAEj6b9JgtzM9ye/5Orul/4r77UJJlIft93UMN3v/vubr7fd1/+UhBl/372u+3v6bvf/yEoMvlcX2HzokPfGElJV1+XFERPFJQ1ntf5KGUubrNwr984fK13wdw83ev6/5evt93X95iMHX/fuar7f/Zu+/vMTgS2Wx/WPGSK+9Jn355eXHDkfxNQ1ltf/tZdLqDTDG6MyZM9f9uj17ciRJ776bo9DQ0o6q5Pbvz9M77+Rc12tKc1hp//48zZ59ff3fiKtjP3AgT3PmeK//q5W0/7IayjtwIE9z55bd9l8r7gMH8jRvnu/2v1UM3ho+PXAgT+++W3r74HrjPngwT++957tjUNi/t/Z3Uf2///7P3/4bjfvgwTzNn++b/V8Y+6FDeVqwwHfnwPX2X9rnyqFDecrMLPvtLy7uQ4fy5HT6dv9b9V/W783Dh/P0wQdls/0ljf3w4Tx9+KHvjsHV/Xv77+Hhw3n6n/+5se3Pz5cOHJCCg6XkZOm99y4v37Tp8u+wsP9eerWg4PJPzv/fZV5ennJyrr//iIgI2Sx2ls0Yb5ROlFxOTo4iIyN9HQYAAABw08jOzpbD4Sj2+XKXNPzckYbTp3NUu/Yt+vbbA4qIKH6Dy5vytfevj7/GTtze56+xEzdKyl/3OXF7l7/GLflv7P4at80mRUdLP/4ozZolpaVJ48dLW7dermXo1Ek6fVratk1q2VI6eFD69tsb6/NaIw3lbnqSzWazzHKuJTbWcUOvBwAAAMqDqlUvJw2S9OGHl6cnBQZeLoT+6afLy4OCpICAy3UOZYlCaAAAAKCcq1//8u/w8MuJAzd3AwAAAOCmQYPLv8PCSBoAAAAAFKFwpCEs7PJ0pCvv08AdoQEAAACoXr3LvwtHGgqTBm8haQCu0z//+U/17t1b8fHxstls+uSTT9yeN8Zo/Pjxio+PV2hoqDp27Khdu3b5KFpUNFOmTNEvf/lLRUREqEaNGrrrrrv07VWXzMjNzdXw4cMVHR2t8PBwpaWl6eDBgz6KGBXNzJkz1bRpUzkcly880rp1a3322Weu5zn/4G1TpkyRzWbTiBEjXMsq4nlYubIUH//fmobCpCHAS5/mSRqA63Tu3DmlpKTo9ddfL/L5qVOnavr06Xr99de1adMmxcbGqlu3bj/rUsLA1dauXauhQ4dq48aNWrFihfLy8vTrX/9a586dc60zYsQILVy4UE6nU59//rnOnj2rXr16Kb9wAixwA2rWrKmXXnpJmzdv1ubNm9W5c2f95je/cX05wvkHb9q0aZP+9re/qWnTpm7LK+p5WL++72oaZCqI7OxsI8lkZ2f7OhTcRCSZhQsXuh4XFBSY2NhY89JLL7mWXbhwwURGRppZs2b5IkRUcMePHzeSzNq1a40xxmRlZZmgoCDjdDpd6xw6dMgEBASYZcuW+SpMVHBVq1Y1b7/9NucfvOrMmTOmfv36ZsWKFaZDhw7mySefNMZU7L+DH31kzIIFxjz0kDExMcZIxnTsaExcXNn3zUgDUIr27t2ro0eP6te//rVrWaVKldShQwd98cUXPowMFVV2drYkqVq1apKkLVu26NKlS27nYHx8vJo0acI5iFKXn58vp9Opc+fOqXXr1px/8KqhQ4eqZ8+e6tq1q9vyinwe/va3UkaGeyG05J1C6HJ3czfAnx09elSSFBMT47Y8JiZGP/74oy9CQgVmjNFTTz2lO+64Q02aNJF0+RwMDg5W1apV3daNiYlxnZ/AjdqxY4dat26tCxcuqHLlylq4cKEaN26sbdu2cf7BK5xOp77++mtt2rTJ47mb4e/glTUN3pqeRNIAlIGrb8NujLG8NTvwcwwbNkzbt2/X559/fs11OQdRmho2bKht27YpKytLH330kfr376+1a9cWuz7nH0rTgQMH9OSTT2r58uUKCQkp8esq0nl4ZU0DhdCAH4qNjZUkj28yjh8/7jH6ANyI4cOH63//93+1evVq1axZ07U8NjZWFy9e1OnTp93W5xxEaQoODla9evXUsmVLTZkyRSkpKZoxYwbnH7xiy5YtOn78uFq0aCG73S673a61a9fqL3/5i+x2u2JiYir8ecjN3QA/V6dOHcXGxmrFihWuZRcvXtTatWvVpk0bH0aGisIYo2HDhunjjz/WqlWrVKdOHbfnW7RooaCgILdz8MiRI9q5cyfnIMqMMUa5ubmcf/CKLl26aMeOHdq2bZvrp2XLlurTp4/r3xX9PLy6psEbmJ4EXKezZ8/q+++/dz3eu3evtm3bpmrVqqlWrVoaMWKEJk+erPr166t+/fqaPHmywsLC9MADD/gwalQUQ4cO1YIFC7Ro0SJFRES4RrUiIyMVGhqqyMhIDRo0SKNGjVJUVJSqVaum0aNHKzk52aNYEPg5/vCHPyg1NVW33HKLzpw5I6fTqTVr1mjZsmWcf/CKiIgIVx1XofDwcEVFRbmWV/Tz8OqaBgqhgXJo8+bN6tSpk+vxU089JUnq37+/5s6dq2eeeUbnz5/X448/rtOnT6tVq1Zavny5IiIifBUyKpCZM2dKkjp27Oi2fM6cORowYIAk6dVXX5Xdbtf999+v8+fPq0uXLpo7d64CAwO9HC0qomPHjqlfv346cuSIIiMj1bRpUy1btkzdunWTxPmH8qGin4eBgf9NFLw1PclmjDdyk7KXk5OjyMhIZWdny+Fw+DocAAAAoEyMGSO99NLlf/foIW3dKpX1haGoaQAAAAD8yJUDJhRCAwAAAPBw9WVWvTFviKQBAAAA8COMNAAAAACwRNIAAAAAwBJJAwAAAABLV9Y0kDQAAAAA8HD1SAOF0AAAAADcMD2pFKSnpystLU2ZmZm+DgUAAAAodb5IGuze6cZ7nE4nd4QGAABAhcVIAwAAAABLFEIDAAAAsEQhNAAAAABLTE8CAAAAYImkAQAAAIAlahoAAAAAWGKkAQAAAIAlCqEBAAAAWLoyafAWkgYAAADAj1yZNAR46dM8SQMAAADgRyiEBgAAAGCJQmgAAAAAliiEBgAAAGCJQmgAAAAAliiEBgAAAGCJQmgAAAAAliiEBgAAAGDp6poGCqEBAAAAuGGkAQAAAIClK2saKIQGAAAA4IGRBgAAAACWqGkAAAAAYImRBgAAAACWuLkbAAAAAEvc3A0AAACApatrGryhwiUN6enpSktLU2Zmpq9DAQAAAErd1TUN3iiEtpd9F97ldDrlcDh8HQYAAABQJiiEBgAAAGCJmgYAAAAAlhhpAAAAAGCJpAEAAACAJV8UQpM0AAAAAH6EkQYAAAAAliiEBgAAAGCJkQYAAAAAlkgaAAAAAFiiEBoAAACAJWoaAAAAAFhiehIAAAAAS4w0AAAAALimwtEGkgYAAAAARboyaaAQGgAAAICHAC9/iidpAAAAAPxM4UiDt5IHkgYAAADAz1DTAAAAAMASSQMAAAAAS1feq4FCaAAAAAAeCmsZqGkAAAAAUCSmJwEAAACwRNIAAAAAwNKVNQ3eQNIAAAAA+JnCWgbuCP0zpaenKy0tTZmZmb4OBQAAACgT3r65m9073XiP0+mUw+HwdRgAAABAmaGmAQAAAIAlahoAAAAAWLpypIGaBgAAAAAeriyE9kp/3ukGAAAAQGnxdiE0SQMAAADgZyiEBgAAAGCJQmgAAAAAlri5GwAAAABLTE8CAAAAYImkAQAAAIAlkgYAAAAAlkgaAAAAAFiiEBoAAACAJUYaAAAAAFgiaQAAAABgiaQBAAAAgKUraxq80p93ugEAAABQWgpHGiQKoQEAAAAU4cqkwRtIGgAAAAA/ExjovalJEkkDAAAA4HcKkwZqGgAAAAAUKSCAkQYAAAAAFiiEBgAAAGCJmgYAAAAAlqhpuEHp6elKS0tTZmamr0MBAAAAyoS3Rxrs3uvKO5xOpxwOh6/DAAAAAMoMhdAAAAAALFEIDQAAAMAShdAAAAAALFEIDQAAAMASNQ0AAAAALF1Z0+ANJA0AAACAn7mypoFCaAAAAAAeKIQGAAAAYIlCaAAAAACWArz8KZ6kAQAAAPAzNWpI0dGX/01NAwAAAAAPDz4obd3qvf5IGgAAAAA/ExgoRUZ6rz+SBgAAAMBPUQgNAAAAoFwgaQAAAAD8GIXQAAAAAHyOpAEAAACAJZIGAAAAwE/5TSH0gAEDZLPZ3H5uv/320ojNxel0ymaz6a677irVdgEAAABcm700GunRo4fmzJnjehwcHFwazUqSfvzxR40ePVrt2rUrtTYBAACAisJvCqErVaqk2NhY10+1atXcns/OztbgwYNVo0YNORwOde7cWd988801283Pz1efPn00YcIE1a1btzRCBQAAAHCdSiVpWLNmjWrUqKEGDRrokUce0fHjx13PGWPUs2dPHT16VEuXLtWWLVt02223qUuXLvrpp58s2504caKqV6+uQYMGlUaYAAAAQIXirZqGG56elJqaqvvuu0+JiYnau3evnn/+eXXu3FlbtmxRpUqVtHr1au3YsUPHjx9XpUqVJEmvvPKKPvnkE/3973/X4MGDi2x3/fr1euedd7Rt27YbDREAAADADbiukYb58+ercuXKrp9169bpd7/7nXr27KkmTZqod+/e+uyzz/Tdd9/p008/lSRt2bJFZ8+eVVRUlNtr9+7dqz179mj//v1uyydPnqwzZ86ob9++euuttxQdHV0mGw4AAACgZK5rpCEtLU2tWrVyPU5ISPBYJy4uTomJidq9e7ckqaCgQHFxcVqzZo3HulWqVFGVKlXcRhOqVaumPXv2aN++ferdu7dreUFBweWA7XZ9++23SkpKKjLG9PR02e3um5WRkaGMjIySbygAAAAAl+tKGiIiIhQREWG5zqlTp3TgwAHFxcVJkm677TYdPXpUdrtdtWvXLvI19erVc3scFhamHTt2uC0bO3aszpw5oxkzZuiWW24ptn+n0ymHw1GCrQEAAABQEjdU03D27FmNHz9e99xzj+Li4rRv3z794Q9/UHR0tO6++25JUteuXdW6dWvdddddevnll9WwYUMdPnxYS5cu1V133aWWLVt6tBsSEqImTZq4LatSpYokeSwHAAAAblZ+UQgdGBioHTt26N1331VWVpbi4uLUqVMnffDBB64RCZvNpqVLl+q5557TQw89pBMnTig2Nlbt27dXTExMqWwEAAAAgLJjM8Ybt4Moezk5OYqMjFR2djbTkwAAAHBTeOcd6eGHy/4Gb6VynwYAAAAAvkPSAAAAAMCnSBoAAAAAP+WtQmiSBgAAAACWSBoAAAAAWCJpAAAAAPwchdAAAAAAfIqkAQAAAPBTFEIDAAAAKBdIGgAAAAA/R00DAAAAAJ8iaQAAAABgiaQBAAAA8FMUQgMAAAAoF0gaAAAAAD9HITQAAAAAnyJpAAAAAPwUNQ0AAAAAygWSBgAAAACWSBoAAAAAP0chNAAAAACfqnBJQ3p6utLS0pSZmenrUAAAAIAy5a1CaLt3uvEep9Mph8Ph6zAAAACACqPCjTQAAAAAKF0kDQAAAICfoxAaAAAAgE+RNAAAAAB+ijtCAwAAACgXSBoAAAAAWCJpAAAAAPwchdAAAAAAfIqkAQAAAPBTFEIDAAAAKBdIGgAAAABYImkAAAAA/ByF0AAAAAB8iqQBAAAA8FMUQgMAAAAoF0gaAAAAAFgiaQAAAAD8HIXQAAAAAIpETQMAAACAcoGkAQAAAIAlkgYAAADAz1HTAAAAAMCnSBoAAAAAP0UhNAAAAIByocIlDenp6UpLS1NmZqavQwEAAAAqBLuvAyhtTqdTDofD12EAAAAAXkMhNAAAAACfImkAAAAA/BSF0AAAAPj/2rt/0KbWMA7Ab7UgoqmhCka6CAq6WUpARCiCSrkIoZvp4BAHBxdBcOqgi1ZBcNPZfzSDlOIQroMoKDhIoeggHUQppRSFQtSCdTB3usVy46k1jcnpfR4o9JTzfXmz9ceXXw60BaEBAABIJDQAAEDKKUIDAAAtJTQAAEBKKUIDAABtQWgAAAASCQ0AAJByitAAAEBLCQ0AAJBSitAAAEBbEBoAAIBEQgMAAKScIjQAAFCXTgMAANAWhAYAACCR0AAAACQSGgAAIOUUoQEAgLoUoQEAgLYgNAAAAImEBgAASDmdhlUqFotRKBRidHS01aMAAMC60NnqAdZauVyOrq6uVo8BAABNpwgNAAC0BaEBAABIJDQAAEDKKUIDAAAtJTQAAEBKKUIDAABtQWgAAAASCQ0AAJByitAAAEBLCQ0AAJBSitAAAEBbEBoAAIBEQgMAAKScIjQAAFCXTgMAANAWhAYAACCR0AAAACQSGgAAIOUUoQEAgLoUoQEAgLYgNAAAAImEBgAAIJHQAAAAKacIDQAA1KUI/ZuKxWIUCoUYHR1t9SgAALAudLZ6gLVWLpejq6ur1WMAAMC6se5OGgAAgLUlNAAAQMopQgMAAHUpQgMAAG1BaAAAABIJDQAAkHI6DQAAQEsJDQAAkFKK0AAAQFsQGgAAgERCAwAApJwiNAAAUJdOAwAA0BaEBgAAIJHQAAAAJBIaAAAg5RShAQCAuhShAQCAtiA0AAAAiRoODWNjYzEwMBA7duyIjo6OmJycXIu5YmxsLPL5fGSz2diyZUv09vbG3bt312RvAADg1zUcGhYWFuLw4cNx9erVtZhnSXd3dwwPD8eLFy/i1atXUSqVolQqxaNHj9b0dQAAIO2aXYTubHSDU6dORUTE+/fvf3pPtVqNCxcuxPj4eHz9+jXy+XzcuHEjDhw48NM1R44cWXZ97ty5uH37djx//jwGBgYaHRsAAFJv3RSha7VanDhxIubm5qJSqcTExET09fXF0aNHY35+/pf3ePz4cUxNTUV/f3+TJwYAAH7U8EnDSp48eRKvX7+ODx8+xKZNmyIi4vr16zE+Ph4PHjyIM2fO/HRttVqNnp6eWFxcjI0bN8bNmzfj+PHjzR4ZAAD4wapOGu7fvx9bt25d+nn27NmKayYmJuLLly+xffv2ZWvfvXsXb9++jenp6WV/v3LlytLaTCYTk5OT8UyB+dAAAAIDSURBVPLly7h8+XKcP38+nj59uuo3CQAA/L5VnTQUCoU4ePDg0nVPT8+Ka75//x67du2q+89+NpuNbDa77BuXuru7l37fsGFD7N27NyIient7482bNzEyMvKfvsOPisVidHYuf1tDQ0MxNDS04qwAAJBGbVWEzmQykclkVvUCfX19MTc3F52dnbF79+669/wbDFZSq9VicXEx8Z5yuRxdXV2rmhEAANLoTxWhG+40zM/Px/T0dMzOzkZExNTUVERE5HK5yOVycezYsTh06FAMDg7GtWvXYt++fTE7OxuVSiUGBwcjn8/X3XdkZCTy+Xzs2bMnvn37FpVKJe7cuRO3bt1qdGQAAGAVGg4NDx8+jFKptHRdLBYjIuLixYtx6dKl6OjoiEqlEsPDw3H69On4+PFj5HK56O/vj507d/5034WFhTh79mzMzMzE5s2bY//+/XHv3r04efJkoyMDAACr0FGrNfsTUH/Gp0+fYtu2bVGtVn08CQCA/4W//47466+ImZmIX6gb/7amP6cBAABormYfAwgNAACQUuvmidAAAEC6CQ0AAEAioQEAAFKurR7uBgAAtI+BgeYHhoh19JWrtVotPn/+HJlMJjr+VCMEAAD+B9ZNaAAAAJpDpwEAAEgkNAAAAImEBgAAIJHQAAAAJBIaAACAREIDAACQSGgAAAAS/QPcu8iKjN7BYwAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "error_squar_norm_null_plunging = []\n", "error_e_null_plunging = []\n", "error_l_null_plunging = []\n", "\n", "i = 0\n", "for (S,T,R,TH,PH) in sol_null_plunging:\n", " P = geod_IEF(S, interpolation_key='null_plunging_equatorial')\n", " V = geod_IEF.tangent_vector_eval_at(S, interpolation_key='null_plunging_equatorial')\n", " # print(i)\n", " squar_norm_null_plunging = numerical_approx((g.at(P)(V,V)).substitute({m:1}))\n", " e_null_plunging = numerical_approx((-g.at(P)[0,0]*V[0] - V[1]).substitute({m:1}))\n", " l_null_plunging = numerical_approx((g.at(P)[3,3]*V[3]).substitute({m:1}))\n", " # print(i)\n", " if i == 0:\n", " squar_norm_null_plunging_0 = squar_norm_null_plunging\n", " e_null_plunging_0 = e_null_plunging\n", " l_null_plunging_0 = l_null_plunging \n", "\n", " error_squar_norm_null_plunging += [(S, squar_norm_null_plunging\n", " - squar_norm_null_plunging_0)]\n", " error_e_null_plunging += [(S, e_null_plunging - e_null_plunging_0)]\n", " error_l_null_plunging += [(S, l_null_plunging - l_null_plunging_0)]\n", " \n", " i += 1\n", "\n", "plot_error_squar_norm_null_plunging = line(error_squar_norm_null_plunging)\n", "plot_error_e_null_plunging = line(error_e_null_plunging)\n", "plot_error_l_null_plunging = line(error_l_null_plunging)\n", "\n", "plot_error_squar_norm_null_plunging.show(title=\"Null geodesic - Plunging trajectory: error on conservation of \" +\n", " \"squared norm\", ymin=-1e-3, ymax=1e-3)\n", "plot_error_e_null_plunging.show(title=\"Null geodesic - Plunging trajectory: error on conservation of e\",\n", " ymin=-1e-3, ymax=1e-3)\n", "plot_error_l_null_plunging.show(title=\"Null geodesic - Plunging trajectory: error on conservation of l\",\n", " ymin=-1e-3, ymax=1e-3)\n", "\n", "plot3D_projected_geod_IEF_null_plunging = geod_IEF.plot_integrated(interpolation_key='null_plunging_equatorial',\n", " mapping=IEF_spatial_coords,\n", " plot_points=200,\n", " thickness=2,\n", " display_tangent=True,\n", " plot_points_tangent=10,\n", " scale=0.5,\n", " width_tangent=1,\n", " label_axes=False)\n", "\n", "(plot3D_projected_geod_IEF_null_plunging + plot3D_event_horizon + plot3D_origin).show(viewer='threejs',\n", " online=True)" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.3", "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": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 2 }