{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Null geodesics in Schwarzschild spacetime\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://relativite.obspm.fr/blackholes/).\n", "\n", "Click [here](https://raw.githubusercontent.com/egourgoulhon/BHLectures/master/sage/ges_null_geod.ipynb) to download the notebook file (ipynb format). To run it, you must start SageMath with `sage -n jupyter`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A version of Sage at least equal to 9.0 is required to run this notebook:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.1.beta0, Release Date: 2020-01-10'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Schwarzschild metric" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (M, (t, r, th, ph))" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = Manifold(4, 'M', structure='Lorentzian')\n", "X. = M.chart(r't r:(0,+oo) th:(0,pi):\\theta ph:(0,2*pi):periodic:\\phi')\n", "X" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = (2/r - 1) dt*dt - 1/(2/r - 1) dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = M.metric()\n", "m = 1\n", "g[0,0] = -(1-2*m/r)\n", "g[1,1] = 1/(1-2*m/r)\n", "g[2,2] = r^2\n", "g[3,3] = (r*sin(th))^2\n", "g.display()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t = t\n", "x = r*cos(ph)*sin(th)\n", "y = r*sin(ph)*sin(th)\n", "z = r*cos(th)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Xcart. = M.chart()\n", "X_to_Xcart = X.transition_map(Xcart, [t, r*sin(th)*cos(ph), r*sin(th)*sin(ph), r*cos(th)])\n", "X_to_Xcart.display()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (M, (t, r, th, ph)), Chart (M, (t, x, y, z))]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.top_charts()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (M, (t, r, th, ph))]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M._top_charts = [X]\n", "M.top_charts()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate functions (t, r*cos(ph)*sin(th), r*sin(ph)*sin(th), r*cos(th)) on the Chart (M, (t, r, th, ph))" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.identity_map().coord_functions(X, Xcart)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Some selected null geodesics" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def initial_vector(r0, b, ph0=0, E=1, inward=False):\n", " t0, th0 = 0, pi/2\n", " L = b*E\n", " vt0 = 1/(1-2*m/r0)\n", " vr0 = sqrt(E^2 - L^2/r0^2*(1-2*m/r0))\n", " if inward:\n", " vr0 = - vr0\n", " vth0 = 0\n", " vph0 = L / r0^2\n", " p0 = M((t0, r0, th0, ph0), name='p_0')\n", " return M.tangent_space(p0)((vt0, vr0, vth0, vph0), name='v_0')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The photon orbit" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "b = 5.196152422706632 m\n" ] } ], "source": [ "r0 = 3\n", "ph0 = 0\n", "b = 3*sqrt(3)\n", "E = 1\n", "print(\"b = {} m\".format(float(b)))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v_0 = 3 d/dt + 1/3*sqrt(3) d/dph" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v0 = initial_vector(r0, b)\n", "v0.display()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p0 = v0.parent().base_point()\n", "g.at(p0)(v0, v0)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Integrated geodesic in the 4-dimensional Lorentzian manifold M" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = var('s')\n", "geod = M.integrated_geodesic(g, (s, 0, 100), v0)\n", "geod" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "sol = geod.solve(step=0.01, method=\"ode_int\") # numerical integration\n", "interp = geod.interpolate() # interpolation of the solution for the plot" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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OlHzb/IKZy1sRkU1dWDQtN5oncfhJ3w5VDVUI/0e4fNv0ggkaDb/9EZHtWRbNWkNtiw0cSAwWTCs1mZoQ+EagfNv4vJE9SyKyK8uimVmUiVu/v1VgGuInvhWMZiN0r+jk2w3PNvCcpYt5/fXXkZKSAj8/P4SFheH6669HTg7XACX7syya3xz8Bq9uflVgGtfGgtkGSZLg8fL52a/V86rh6e55mUeQM9q0aRPmzp2LnTt3Yv369TAajZg4cSLq6upERyMXYFk0n9v4HNYcXSMwjeviSj9tsJyhdurxU4jyi7rMb5OrKC0tRVhYGDZt2oQxY8ZY9Riu9EOdZfl5dOyRY+gV1EtgGtfjLjqAklm+OdPvS2exJFlVVRUAIDAwEDU1NS3+NDQ0wGw2o6GhAY2NjTCbzTCZTHJv9LfffoOfnx/c3NzkPx4eHvD19YWfnx/8/Pzg6+sLnU53uQjkgqQXJflzqfe/eqP26Vp00XURnMp1sId5CZbFcvGfFuPPw/4sMA2J0NDQgPLyctTW1rYoiNXV1fjHP/6Buro63HDDDTAajTCZTDAajTCbzfDwODeEf/jwYWRnZ0Oj0ch/JEnCddddB61WC0mS5D8mkwmSJEGr1UKr1cLd3R3e3t4IDAxEUFAQ/P395WLaXFADAwMREBDAmdouRpIkuL10/mxa0/NNcHdj38cRWDBbkbIkBZlFmQCAib0nYu3stYITkb01NDSguLgYxcXFOHXqFAoKClBcXAyDwQCTyQSz2QydTgdPT08cPHgQZWVlmDp1KkJDQ+Hj4wNvb2/4+PjAy8sLbm7nPsyaC2mzxsZGvPvuu5g3bx48PVueB5ckCU1NTaivr4der0d9fb3c1uv1aGhogMFgQGNjo1xY3d3dERAQgB49eiA6OhpRUVGIjIxEYGAgi6iTazQ2wutVL/m2+QUz/80dgF9LLvDRno/kYgmAxdIJXao4Ng+f+vn5ITAwEHFxcQgKCoKPjw88PT3h5uaGX375BVqtFk899RSCgoIuexx3d3e4u1v3X0yj0UCn00Gn0yEwMPCSv9dcWPV6Paqrq1FeXo68vDz88ccfMBqN0Ol0LYpoZGQkoqKiWESdjKe7J/IeyUOvf507h+n2kttFix2Q7bFgWsgtz8Wcn+bIt/kGdA719fXIzc3F0aNHkZ+fj5KSklaLY0hICAICAuQeoiVJkrB69WpkZ2fjzjvvbLNY2otlYQ0ICEBMTIz8M71ej/LycpSVlV2yiMbGxiIuLg7h4eEsoCoXGxSLpdctxd0r7wZw7jQSP7Psi0Oy/3PhEAffeOpWVlaGnJwcHDp0CEeOHEF9fT18fHwQEhKCkJAQhIaGwt/fv9Xi2Jqff/4Z+/fvx6233orQ0FD5fk9PT/mcZVsaGxuxYMGCVodk7cWyiJ49exYVFRVwd3dHREQEBg0ahLi4OPTs2RNaLa8rVquERQk4XHYYAHBD/xvww80/CE7kvFgw/8dykg/PB6iP2WxGQUEBcnJycODAARQWFsJgMCA4OBgxMTGIjo6Gt7d3h59//vz5rd5/3XXXITEx0arnEFEwL2QymXD69GkUFBSgpKQEJpMJgYGBGDhwIOLj49G3b99OvU4khuXn154/70FSZJLANM6LBRMt32wlT5Qg3Df8Mr9NStHY2Ihjx44hOzsb+/fvx9mzZwEA4eHhiImJQWRkpNXnEB1BCQXTkiRJqKioQEFBAYqKilBbWwtfX1/069cPCQkJ6NevH0JCQkTHJCtZfo41PNvABVbsQDmfJoJM+nyS3F44eSGLpcJJkoTjx49j165dyMrKQk1NDby9vREZGYmEhASEhoZydMBKGo0GwcHBCA4OxpAhQ1BfX4+CggKcOHECe/fuhU6nQ8+ePZGWloYhQ4bAy8ur7SclYSyv0fR61YunlezApXuYuwp3YfjHw+XbfIMpl16vx759+7B9+3bk5+fDw8MDvXr1Qvfu3eHr6ys6nlWU1sO8nKamJhQXFyMvLw+lpaUICgpCWloaUlJSEBER0fYTkBBVDVUtNongZ5ptuWwPs76pnsVSBYqLi5Geno709HRUVVWha9euGDFiBGd52pmHhwe6d++O7t27y7OMN2zYgI0bNyI+Ph7Dhw9HQkKCooa8CQjwCsC/r/03Hlz9IAAgbmEcch7iJgG24rI9TMvxfhZLZTEajTh48CB27tyJ7OxsSJKE2NhY9OvXT9UTUtTUw2yN5cSq6upqREREYPjw4UhOTr7staPkeJafb3vv34vECOsmptHluWTBtHwzVTxVgUAv/mdXgoqKCmRmZmLnzp04ffo0AgICEBcXh+joaKsv/1AytRdMS1VVVcjJyUFBQQG8vLwwZMgQpKWloU+fPuz5K4Tl55zpBRP377UBlxtPeWnTS3L71XGvslgqQHl5OX799VdkZGSgoaEBMTExuPrqqxEQECA6Gl1CQEAAUlNTkZSUhOPHj2Pfvn1IT09HbGwsJk6ciISEBBZOwcwvmOU1Z7UvaTmSZgMu1cOsNdTC73U/+TbfQGLV1NTg999/x9atW9HY2Ij+/fujd+/eTndeLD09HRkZGZAkCeXl5U7Rw7yQJEkoKytDVlYWqqqq0L9/f0yaNAm9enH7KZEOlR7CgH8PkG/zM69zXKpg8rylMuj1emzbtg0bN25EdXU14uPjER8f7/SrzTjTkOzllJSU4I8//kBDQwMSExMxceJEREVxazxRgt4IQmVDJQBg5707kRadJjiRerlMweRFveI1NTUhPT0dGzZsQGlpKXr16oWBAwe6zL6PrlIwgXM9zoKCAmRlZcFsNiMtLQ3jx49vsawgOQ7PZ9qGc419XcK3B7+V2wvGL2CxdDCz2Yy9e/di3bp1OHXqFKKjozFlyhRVz3ily9NoNOjevTuio6ORl5eHHTt2YM+ePRg1ahSuvPJK+Pv7i47oUng+0zacvofZZGqC7pXzPRi+URxHkiQcPnwY69atw9GjRxEWFobExESX/bB0pR7mhUwmE7Kzs5GTkwNfX1+MGzcOo0aN4pcmB9p0YhOu/ORKAMADwx7AB3/6QGwgFXL6gsnzlmKUlpZixYoVOHDgAPz9/TF06FAEBweLjiWUKxfMZgaDAQcPHkReXh5CQ0MxdepUJCUlcUatg1h+HlbPq4afp99lfpsu5NRDsg/+/KDc5moXjmE2m7F9+3b8/PPPaGxsxIgRIxAZGSk6FimETqdDUlIS4uPjsXv3bixbtgz79+/H9ddfz8uIHMByvVn/Bf7sRLST0xbMOkMdPsg8P+TQL6SfwDSuobS0FD/88AMOHjyIHj16IDEx0ekuESHb8Pb2xujRo1FYWIiMjAzk5eXhuuuuY2/TAc4+eRbBb54b7eGm0+3jtJ9mvq+fX5Cbbwj7urBXOWbMGHTt2lV0LFKB6OhohIWFIT09nb1NBwnyDoK/pz+qG6sBACW1JYjw5YL61nDKgjnj2xly+/T/nRaYxPmxV0mdpdPp2Nt0sKp5VfLQbOTbkexUWMnpLsapb6rH8sPL5dthXcIEpnFeZrMZW7duxTvvvIPc3FyMGTMGycnJLJbUYc2XG3l4eGDZsmX49NNPUVVVJTqW06p7pk5uByxgj94aTvfp1uW1LnKb35rsg71Kshf2Nh3Hx8MHAZ4BqGqsQnVjNRqMDfBy5ybhl+NUPcxvDnwjt/P/mi8wiXOSJAk7d+6Ue5VXXHEFe5VkFxf2Nj/77DPU19eLjuV0KudVym3vV3lNbFucpmBKkoRbf7hVvt09oLvANM7HaDRixYoV+PLLLxEUFIRrr70WYWEc7ib7ae5tpqamIjMzE4sWLcLp05yTYGulfyuV2w+vflhgEuVzmoULuECB/dTU1ODLL7/E/v37kZSUhN69e4uOpCqusFuJvdXW1mLTpk3w8vLCrFmzEB8fLzqSU7H8/DQ+b4TWzbk3Qugop+hhHi49LLdX3LJCYBLnc+rUKSxcuBCHDh3C2LFjWSw7IDU1FXPnzsWcOXNER1EtX19fTJw4EVqtFkuWLMHmzZvhJN/1FcGyk+H+Mk+xXIpTFMyEfyfI7evjrxeYxLlkZWVh0aJFqKysxKRJk3htJQnl4eGBsWPHIiYmBt999x2+++47GAwG0bGchmVnI7ssW2AS5VL9V4krll4ht00vmAQmcR5msxm//fYbfv75Z4SEhGDEiBFOv1clqYNGo0FiYiKCgoKwZcsWlJaWYvbs2VzowAYsOxv9F/Xnqa1WqLqHaTKbsPXkVgBAiHcI93izgcbGRnz55Zf48ccf0adPH4waNYrFkhSnR48euOqqq3DkyBG8//77OHnypOhITsH4vFFuWy4AQ+eousJYjrWXPVkmMIlzKC8vx4cffohdu3ZhxIgRGDBgAK99I8UKDg7GpEmTUF9fjw8++AB79uwRHUn1LCf7LD+8nOeJL6DagllSWyK3f73jV4FJnENeXh4WLVqE/Px8TJgwAd26dRMdiahN3t7eGD9+PPz9/fHpp59i9erVMJvNomOpmuVQbPOm03SOal+NyLfPbxk1LnacwCTql52djSVLlqCxsRHXXHMNzweRqmi1WowYMQLx8fH45Zdf8MMPP8Bk4nyGznh/8vtyu6qByxM2U2XB/PrA13K7/hmu/tEZBw8exNKlS+Hp6Ylx48ZBp9OJjkTUIfHx8Rg2bBg2bdqEb7/9lkWzEx5KfUhuB74RKDCJsqiyYN72w21y29uDyzl11L59+7Bs2TL4+vpizJgxnNxDqtezZ0+kpaVh27Zt+Oqrr2A0Gtt+ELWq8LFCuW15rbsrU91lJbd8f4vc5rTnjtuzZ4+8zN2IESPg5qbK705EF4mJiYGbmxt27NgBo9GIWbNmwcPDQ3Qs1enmf34eQ8K/E/h5CxX2ML89+C0AwMON/wE6KjMzE59//jlCQkIwcuRIFktyOt26dcPo0aOxe/dufPbZZ2hqahIdSZWanj//uv1n938EJlEGVX1SBr0RJLcNz3OFj47Yu3cvvvzyS4SHh2P48OG8bIScVkREBEaPHo29e/fiiy++4PBsB7i7nR+EvP+/9wtMogyqGZKVJAmVDee2orkx4UbBadRp//79+OKLL9C1a1ekpqayWDqI5eLr5Fjh4eEYNWoUtm7dCnd3d9x22208V99O0ouSvDj7nFVzsGTaEsGJxFHNbiXcjaRzDh06hGXLlsHf3x+jRo1isRSgsbERCxYs4G4lApw6dQo7duzAqFGjcPPNN7NothM/f89RxZCsZU1/cuSTApOoU25uLj755BN06dIFI0eOZLEkl9OtWzekpaVh69atWL58ORc3aCfLIjntq2kCk4iliiFZy9Um3rj6DYFJ1KewsBDLli2Dl5cXRo8ezQk+5LJiYmJgMpmwefNm+Pr6YvLkyaIjqdJPuT+JjiCM4j89LXuXz17xrMAk6lNdXY3PPvsMJpOJ11kS4dx1mgMGDMDatWu59mw7WfYy7155t8Ak4ii+YFrOjH1l3CsCk6hLU1MTvvzyS5SUlODKK69ksST6n/j4eISHh+O7777jLicdtOyPZaIjCKH4glnVeG4dwzlDuVu9tSRJwqpVq3DgwAGMGTMG3t5cDYnIUvMs8c8++wxVVVwr1VqWvcxnfn1GYBIxFF0wx31yflH1/0zlRbPW2r59OzZt2oRhw4YhJCREdBwixdFqtbjiiitQWlqKzz//HAYDr+tur9e3vi46gsMpumBuPLERADA4fLDgJOpx5MgRrFixAj169EBsbKzoOESK5e3tjTFjxiA7Oxs//vgjr5O1kmUvc8XhFQKTOJ5iC+a8DfPk9r4H9glMoh7N35Z9fHwwdOhQ0XGIFC84OBjJycnYsmULtmzZIjqO6tzw7Q2iIziUYgvmG9t4+Uh76PV6fPrpp6irq8Po0aN5rSWRlXr06IHevXtj5cqVyM7OFh1HFYzPn19msLC68DK/6VwUWTA352+W2668qoS1zGYzvv32W5w4cQJjxozhnpZE7TRkyBD4+fnhiy++wOnTp0XHUTyt2/lZ9zHvxghM4liKLJhjl40VHUFV1q9fj4yMDIwcORL+/v6i4xCpjkajwahRo9DQ0IDPPvsM9fXcmL4tpx4/Jbf1TXqBSRxHcQWzvun8G1X/rGv8I3TGoUND9VVHAAAgAElEQVSHsGbNGgwYMACRkZGi41Ar0tPTsWjRIixZ4rqLVquBh4cHxo4di5MnT+L777/nJKA2RPlFyW2f13wEJnEcxRXMLq91kdte7l4CkyhfXV0dfvjhBwQEBCA+Pl50HLqE1NRUzJ07F3Pm8FpipfP19UVqaioyMzOxd+9e0XEU75+T/ik6gkMpqmBafqPbds82gUnU4aeffkJpaSnS0tI4yYfIRqKjoxEWFoaVK1dyUYM2PDr8Ubl9z8p7BCZxDEUVzCuWXiG3R8aMFJhE+Q4ePIidO3ciKSmJK/kQ2VhqaioqKyuxcuVKDs1aaekfS0VHsDtFFcxtBed6ldH+0YKTKFtdXR2WL1+OwMBA9OzZU3QcIqej0+mQkpLCoVkrmF84v1VaaV2pwCT2p5iCebziuNwueKxAYBLl41Askf1xaNY6lp9BYf8IE5jE/hRTMHv9q5foCKrAoVgix+HQrHX23u8avXBFFEzLN+KRh48ITKJslkOxXCeWyP44NGudxIhEuT3tq2kCk9iXIgrmvavuldt9gvsITKJslkOxROQYHJptn59yfxIdwW4UUTBdYXZVZ3EoVrz8/Hx89dVXePvttzF//nyuO+pCODTbNsvJPxX6CoFJ7Ed4wbRc2cfyBafzOBSrDAaDAeHh4bj22mtFRyEH49Bs2ywn/wS/GSwwif0IL5iWK/twxmfrNmzYwKFYBejbty/GjRuH/v37i45CAjQPza5atQp6PZftbM1r414THcGuhBfMZo+kPiI6giKVlZVh69atiI+P51CsyhiNRjQ2Nrb4Q+o2bNgwlJWVYds2rkTWmqeveFpuHzt7TGAS+3AXeXDL4dj3Jr8nMIlyrV+/Hk1NTYiLixMdhdpp69at2LRpk+gYZEPe3t7o1asXNm7ciLS0NPj5+YmOpFh93u/jdNszCi2YlsOxdLHCwkJkZGRg4MCB0Gq1bT+AFGX06NEYMWKEfLuxsRHvvvuuwERkCwMHDsR///tfbNy4EdOmOe8lFB21675dSPvIOU8fKWJI9tsbvxUdQXEkScK6deug0WjQqxcXdVAjd3d3eHp6tvhD6qfT6RAXF4dt27ahvLxcdBzFSe2WKrd/O/6bwCS2J6xg5lXkye2bBtwkKoZiHTt2DFlZWUhMTISbmyK+1xDR/8THx6OxsREbNmwQHUXRxn86XnQEmxL2Sdz7X71FHVrxJEnC2rVr4eXlhehoLkSvFAaDASUlJSgpKQEAVFRUoKSkhBezuyCtVosBAwZg165dKCoqEh1HcQ4+eFB0BLsQ3nX5/qbvRUdQnIMHDyInJwdJSUm81EZBioqKsHjxYixevBgAsG7dOixevBgbN24UnIxE6N27NzQaDdatWyc6iuIkdE2Q2zsLdwpMYltCJv0U1xTL7RkJM0REUCyTyYS1a9ciMDAQ4eHhouOQhZ49e+LFF18UHYMUws3NDUOGDMGePXuQl5fHuQaXMOLjEU4zW1ZIDzPqnSgRh1WFPXv24MSJE0hMTGz7l4lIqJiYGHh5eWHt2rVcMu8CG+90vpEXoUOyL1/1ssjDK47BYMD69esRFhaG4GDnXFqKyJloNBokJibi8OHDOHTokOg4inJlzyvl9qnqU+KC2JDDC2aTqUluPzfmOUcfXtHS09NRVFSEpKQk0VGIyEoREREICAjAunXr2Mu8hOh3nWPyosML5oiPR7T9Sy7IbDZj27ZtiIiIgK+vr+g4RNQOgwYNwokTJ3DsmPMtB9cZdw65U3QEm3J4wdxdvNvRh1SF3NxcnDp1igt7E6lQ165dodPpsGvXLtFRFGXZ9cvkttFsFBfERoSdwzQ8ZxB1aEXatWsXvL29ERISIjoKEbWTRqNBnz598Mcff6CyslJ0HEV6Yu0ToiN0mkML5u6i871LD62HIw+taOXl5cjKykLfvn1FRyE7SE9Px6JFi7BkyRLRUciOevXqhYaGBuzezVG01vwr/V+iI3SaQwtm8pJkRx5ONTIzM9HU1MTNoZ1Uamoq5s6dizlz5oiOQnbk4eGBmJgY7NixA0aj+ocfbeXU484xQxYQNCT772v/LeKwitTU1IQdO3age/fu3JGESOXi4uJQUlLCS0wsRPmdv+6+vF7di9U7rGBaTrf+S8pfHHVYxTtw4ADKysq43yWREwgICEBAQAB27nSe5eBsKfStUNEROsVhBfOrA1856lCqIUkSduzYgaCgIG5ES+Qk+vXrh+zsbHmRfnIeDiuYs5bPctShVKOoqAhHjhxBv379REchIhuJiYmByWRCRkaG6CiK0fBsg+gINuHwc5jLrlvm6EMqVnp6OiRJQrdu3URHISIbcXNzQ2xsLHbt2oWGBucoFJ3l6X5+8/Sy+jKBSTrHIQXT8vzlnYnOtfJDR9XX1yMjIwO9e/fmBtFETqZfv36orKzEvn37REdRnK5vdRUdocMc8kmddTrLEYdRlaysLFRXV6NPnz6ioxCRjfn4+KBr165c+cfJOKRgJi7mVlUXOnDgAIKDg+Ht7S06ChHZQWxsLE6cOIHycnVfSmErpX8rFR2h0xw6Fjg+drwjD6dY9fX1yM3N5blLIicWGRkJg8GA3Nxc0VEUIdTn/CUlBpM6l0Z1aMFcO3utIw+nWEeOHEFdXR1iYmJERyEiO/Hw8EBQUBAXMWjFh5kfio7QIXYvmPVN9XJb68aVbAAgOzsbXbp0gY+Pj+goRGRH0dHRyM3NhV6vFx1FUR5d86joCB1i94L55rY37X0IVTEajTh48CCHY4lcQExMDGpra3HkyBHRURThweQHRUfoFHd7H2D+pvn2PoSq5Ofno7KyEomJnAjlKtLT05GRkdHi8ipyDT4+PvD19UV2djYGDx4sOo5wC69diH9nqnctcYedw3xzAnuaAJCTkwOtVougoCDRUchBuFuJa4uKisKBAwdgMplERxFOo9HIbZNZfa+Hwwrm/438P0cdSrEkScL+/fsRERHR4o1DRM4rJiYGlZWVOHHihOgoivLx3o9FR2g3uxZMs2SW2ywQwOnTp1FSUsLZsUQuJCgoCG5ubsjJyREdRVHu/+/9oiO0m10L5qqcVfZ8etXJycmB0WhEeHi46ChE5CAajQYRERE4cOAAz2MDSIpIEh2hw+xaMKd/M92eT686hw4dQmhoKDeKJnIxMTExKC4uxpkzZ0RHEW7rPVtFR+gwh5zD7ObHSyhqampw7NgxDscSuaCIiAgYjUZkZ2eLjiKcj4d6rz93SMHMmMN94fLz86HX6xEZGSk6ChE5WPPMeE78aam4plh0hHZxSMGM9GORKCoqgk6n42LrRC4qODgYJ06c4HlMC29se0N0hHaxW8FsNDba66lV6dSpU/Dz8xMdg4gECQ0NRVVVFSorK0VHUYz3dr0nOkK72K1g7i7eba+nVh1JkpCfn4/Q0NC2f5mInFJISAgMBgOKi9U1DGkPYV3CREfoELsVzGlfTbPXU6tORUUFqqurERISIjoKEQni7e0Nd3d3FBUViY4i3M57d4qO0CF2K5jlem6a2qyoqAiNjY0smEQuzt/fH6dOnRIdQ7jYoFjRETrE7ouv35N4j70PoXjNE368vLxERyEBuPg6NbOc+MPVz85R02th91myb1ytrllQ9sAJP66Ni69TM078uVhBdYHoCFaze8EM9XHtiS6c8ENEzTjx52Jf7v9SdASrOWy3ElfFCT9E1IwTfy729K9Pi45gNbsUTF6DeR4n/BCRJU78US+7FMwzdVxguBkn/BCRJa74c87QyKGiI7SbXQrm51mf2+NpVamoqIgTfohI1jzxp6qqSnQUoT6c8qHoCO1ml4L5zG/P2ONpVam0tBT+/v6iYxCRQvj5+cFoNLr8TNnkqGTREdqNk37sSJIkVFVVccF1IpJ5e3vDZDKhtrZWdBSh1HLtpSW7FsxBYYPs+fSK19jYiIaGBvj4qHf/NyKyLQ8PD7i5uaGmpkZ0FGonuxbM+VfOt+fTK15tbS1MJhN7mEQk02g00Ol0LJgWjGaj6AhWsWvBnNx3sj2fXvFqampgMpnYwySiFnQ6ncsPyVqqb6oXHcEqdi2YXu6ufSlFc8FkD5OILHl5ebn8LFlLh0sPi45gFbsvvu7Kamtr4ebmBg8PD9FRSCAuvk4X8vb2RkVFhegYivFT7k9Ii04THaNNnCVrRzU1NfD09BQdgwTj4ut0IW9vb5e/rMTSVwe+Eh3BKiyYdlRTUwOdTic6BhEpjI+PD/R6PZqamkRHUYS8ijzREaxi8yFZDjudV1VVxR4mEV3Ex8cHJpMJNTU1CA4OFh3HaVVUVGD+/PkwGo04evQobr75ZsycORN/+9vfIEkSKioq8OyzzyIhIcGq57N5wawxcKp0s8rKSs6QJaKLeHt7w2g0smDakcFgwIMPPoi3334bUVFRyM/PR2xsLFauXIl//vOfOHLkCKZMmYKgoCAsXLjQque0+ZDsWf1ZWz+larFgElFrmnuYvLTEfj788EPcfffdiIqKAnBuZrIkSejZsydiY2NhMpnQt29f3HbbbVY/p817mCyY5xgMBjQ0NPCSEiK6iIeHBzQajcsvXhDqE4qy+jK7PHdQUBAmTpwo387MzAQAXHPNNQCAyZMnY/Lk9q0VYPMeZp2hztZPqUpNTU0wm81wd+eVO0TUkkajgVarhdGojhVu7OWK7lfY7blvv/32Frc3btwIrVaL0aNHd/g5bV4wuRfmOWazGQDg5saJyER0MY1GI39OuKoBXQc47Fi//fYbhg0b1qntFm3+aa6W6cH2ZjabIUmSKlfkJyL7Y8EEov2jHXKciooK7Nu3D1deeWWL+z/66KN2PY/NC+bputO2fkpVYg+TiC5Ho9HAZDKJjiFUuG+4XZ63tLQUqampmD//3AYga9asgdlsRmpqaovf2b59e7ue1+af5rUGzvoC2MMkostjDxMI8gqyy/Nu2rRJXo5Sr9fjm2++QVRUlDwrua6uDo888gj+/ve/t+t52z0jRZKky8/sagTQcK5ZXV3d3qd3GlVVVTAYDDAajWhsbBQdhwQwGo0tehDN7wO+HwiAfB2mK39OmvQmq+uFn5+f1R2QSZMm4d5778WZM2dw//334/XXX0d1dTWeeeYZbNq0CQaDAU8//TS6d+/errwaqZ1L81RXVyMgIKBdB3FV/v7+SEhIgJeXa+/aQkQXO378OPLz80XHUI2qqir4+/sLzdDugtlWD/ONTW/gte2vAQCqnm7f9jUpKSnIyMhwiseUlZVhwYIF2L9/P55++ul2LZG3ZMmSdi/UreTHNDY24t1338Vjjz3mUq/DhT3MmpoafPTRR3jwwQfb9R9fSX8nWzzOGd8PHXncypUr8cEHH6CgoKBd7wdHfeY54lgZpzIw4dMJAICCuZd/HdrTw7SXdg/JajSay/6lYsNigf91qNr7bUCr1TrNY4xGI3Q6HSRJgqenZ7s+GDQaTbvXoFXyY5q52utwqZ870+vQmce5+uvQfI22v79/uz5bHPWZ55BjlaFFvRDdg2yLzSf9dOYk7ty5c53mMZ2ZHZuSkuJUj+koJf+d+Dp0/nGOOI6SX4eOblThqM88RxzLXqv82Eu7h2Tb8vPBn/Gn7/8EAJBedN2dS6qrq/Hss88iPT0dL730kkvvWtLY2IgFCxZg3rx5Lv06VFdXy0ORSv8mbU98P5zz/fffY9GiRYo4NyfKW9vewpMbngQAVD2m/NfB5j1MjTsvowDO9TC1Wi1SU1Oh1WpFxxFKq9Vi7NixfB3+9/fn68D3A3BuCPeuu+5y6S8N+VXnJz2p4XWw+UKnXTy72PopVcnNzQ3u7u5ISkpy+fVk3d3dL1phwxU1vw/4fuD7ATj3GXHvvfeqolDYy/HK43JbDa+DzXuYAV685AQ494+v1Wp5zR0RXcRsNqOpqcnldzP6o+QP0RHaxeYFM8I3wtZPqUparRa+vr7Q6/WioxCRwjQ0NMDNza1TC4E7g6KaItER2sXmBdNP59pvAEtBQUGor68XHYOIFKa+vh7u7u7w9fUVHYXaweYF08fDx9ZPqVr+/v7sYRLRRfR6PbRarcv3MNXG5rMP5s+fD/xvomxQUBCGDRuGV199FWlpabY+lGI1NTXhueeew9dffw0vLy/s3bsXvXr1woQJE1zuP8jhw4exe/duFBUVQa/X4/7770dEBIftXVF+fj62b9+OoqIi1NbW4pZbbkF8fLzoWA61ZcsWZGdnIy8vD7m5uTh69CjefPNNxMXFiY7mcB988EGL2yNGjMALL7yAyZMnC0rUNpv3MPv16ye3t27dip49e2LixIkoLS219aEUq76+Hnv27MGdd96JMWPG4JZbbkF5eTm++uor0dEczmAwICYmBhMmTBAdhQQzGAwIDw/HtddeKzqKMPn5+UhJScHEiRMxc+ZMmEwmTJw4EXV1daKjOVx09Pm9MEeGj8S4ceNw3XXX4eDBgwJTXZ7NC+bMmTPl9oABA/DOO++guroaWVlZtj6UYgUEBGD9+vWYOnUqdDodunXrhsmTJ6O4uBhVVe1bX1fthgwZgrFjx6JXr16io5Bgffv2xbhx49C/f3/RUYSZPXs2EhMT4eXlhbi4OCxduhQnT57E7t27RUdzuKlTp8rt2cNm49VXX4Wvry927twpMNXl2fWCMIPBgP/85z8ICAjAkCFD7HkoRfL19YVGo0FDQ4N8eQl3LnE96enp8t58RMC5Uaju3bvLX6CDg4MFJxJrZPRIfP3116irq8OIESNEx7kkuxZMz0BPRAVFYf369QgNDbXnoRTJz88PWq0WtbW12LBhAwYNGqSKi3PJtlJTU5GamiovCUdkMBjg6+uLxx9/HKNHj8bAgQNFRxJqaI+h8PPxw4oVK5CQkCA6ziV1akj2iy++gK+vr/xny5YtLX7+9KdP45prrsHNN9+MM2fOdCqokl3qdWjejmb58uWQJAlTpkwRnNS+srKy8Nprr8l/uNcfUesaGxuxdOlSZGVlueTchgvt2r4Lf/nLX3DnnXfi0KFDouNcUqd6mNOmTWsx+7Vbt24tfr40fymKPy5G37598fHHH+Ppp5/uzOEU61Kvg6enJzZs2IBu3brh0UcfdfreZVxcXIsT+a42I5jIGmazGRkZGTh69Ch27tzZ4v+Mq0pOTkZycjIyMjLw3nvvYfHixaIjtapTBdPPz++yH4oltSUAzm1j48xLxLX2OjQ1NeG2225DZWUlbr/9dvj4OP/1qe3d35DI1UiShFWrVuHkyZP49NNPERsbKzqSoii9Vtj0HGZdXR1effVVwOIz87777kNhYSFuuukmWx5K0YxGI2688Ubs2bMHs2fPRn19PWprawEA3t7eLrVLg16vR1VVFWpqagAAZWXn9r9rHr4m12EwGHD27Fn5dkVFBUpKSuDt7Y2AANdYg3r16tXYt28fRo0ahbCwMJSUnOtUBAQEuNy6sk8+86RcK/bv34+vv/4av//+O9asWSM22GXYtGBqtVpkZ2fD1+yL2qRzBaK0tBRbtmzBgAEDbHkoRSssLMSqVasAAG+88Qb69u2LzZs3AwDuvPNO9OzZU2A6x8rJycHKlSvl2z/88AMAYOzYsdyxwsUUFRXhk08+kW+vW7cOwLlLj66//npRsRwqMzMTtbW1SE9PxzfffCPfv3TpUtx1113iggmwtW6rXDDHjx+PwYMHY82aNbj66qvFBrsMm28gDZxbgT5pcRIA195EGji3eMPXX3+NGTNmQKPhXqGujBsnEwDs2rULHh4eePzxx0VHEUoz//znoVrqhM0XLgCAQWGD7PG0qhQVFQU3NzdUV1eLjkJEClBRUYGYmBjRMagD7FIwtW6uc46uLZGRkdDpdPK5OyJyXWazGbW1tRddUeDK/pL8F9ERrGaXgmnJ1Vc38fb2Rnh4OMrLy0VHISLBqqqq4ObmhqioKNFRFGPe6HmiI1jN7gVzW8E2ex9C8Xr06IGKigrRMYhIsPLycnh6enLHHgvd/NTT27Z7wbxi6RX2PoTiRUVFoaamxuV720Surry8HJGRkVxT2oKaTuHZdS1ZOsdy4o+rXG9G53HxdWpWUVGBYcOGiY4hnFr/L9ith/nsFc/a66lVhxN/XFtqairmzp2LOXPmiI5CAnHCz3nfHvxWdIQOsVvBvG/offZ6atXhxB8i4oSf82794VbRETrEbgWzR0APez21KnHiD5Fr44Qf9bNbwbRc1Uat49W2xIk/RK6NE34utnrmatER2sXus2QB4KsD3O+tW7ducHNzYy+TyEWVl5eje/fuomMoyqQ+k0RHaBeHFMxZy2c54jCKFhMTg4CAABQWFoqOQkQOptfrUVdXh759+4qOoihuGoeUIJuxa9oYf66X2Mzd3R0DBgzAqVOnREchIgcrKChAly5dWDAB5Jbnio7QYXYtmGtnr7Xn06tOfHw86urqoNfrRUchIgcqLCxEv379XGIj+bbELYwTHaHD7Fow40Pj7fn0qtO3b1/4+PhwWJbIhRiNRpw9exb9+/cXHYU6ya4F03KmbH1TvT0PpQrNQzIFBQWioxCRgxQVFUGn0yEuTr09K3vY/efdoiO0m8POuI76f6McdShFS0hIwNmzZ2E0GkVHISIHKCgoQHR0NEJDQ0VHUZShkUNFR2g3hxXMP0r+cNShFC0uLg46nQ7FxcWioxCRnUmShDNnzmDgwIGioyhCWb26lwe1++LrO+/dieEfD7f3YVQjJCQE0dHRKCgo4K7rLoKLr7uu5vWjORx7TthbYaIjdIrde5hp0Wn2PoSqaDQaDBgwAGfOnOEHqIvg4uuuq6CgAMHBwfxy/D8S1P2Z59CrRk9UnnDk4RQrLi4OkiRx9xIiJ1dcXIxBgwbBzU1dF+jb254/7xEdoUMc+q8Y+16sIw+nWN27d0dwcDBnyxI5sdraWuj1esTH8/K6CyVFJomO0CEOKZi8HrMlNzc3DBw4EEVFRRyWJXJSJ0+ehJ+fH3r37i06iiJ8feBr0RE6zSEFc8vdWxxxGFUZNGgQDAYDh2WJnJAkScjLy8PgwYPh6ekpOo4i3PbDbaIjdJpDCmaoz/nrj5pMTY44pOL16dMHMTExyMnJER2FiGzs9OnTaGpqQloaJz1eaOOdG0VH6DCHn4kOeTPE0YdUJDc3N4wYMQIlJSVoaGgQHYeIbCgnJwc9e/ZEbCznbVzoyp5Xio7QYQ4rmCHe5wpljaHGUYdUvKSkJPj5+eHo0aOioxCRjej1epSWlmLEiBEtlgd1ZdsLtouOYBMOK5iFj3PB8Qt16dIFycnJOHbsGCf/EDmJ3NxcBAQEYMiQIaKjKIazLI3qsILp5e4ltxuMHIJslpqaCuDcAs1EpG5msxnHjx9HamoqvL29RcdRnLeufkt0hE4RcjWt96t8IzWLjo5G7969OfmHyAkUFhZCo9HIX4SppceGPyY6Qqc4tGD2C+nnyMOpgkajwciRI3H27FnU1taKjkNEnZCTk4P4+HhERkaKjqIYH+35SG5r3bQCk3Se3Rdft5QxJwMBCwIceUhVGDhwIEJDQ5GTk4Nhw4aJjkM2xsXXXUNVVRWqqqowfDg3m7A05yfnWUPZoT1Mf09/ub2jYIcjD61oOp0Ow4cPR35+Pkwmk+g4ZGNcfN015OTkIDw8HAMGDBAdRZEOPXhIdIROE7Yi8Mj/N1LUoRUpOTkZHh4eOHHihOgoRNRORqMRBQUFGD58ONzdHTpwp2iWEzz7d+0vMIltOLxgqnmVB3sKDQ3FoEGDkJOTw6E7IpU5duwYvLy8kJycLDqKojjbBE+HF0zLVR64TF5LV1xxBQwGA3cxIVIRk8mEQ4cOISUlBUFBQaLjKNK0uGmiI9iE0E3adK/oRB5ecXr16oUhQ4YgKysLZrNZdBwissLhw4fh5eWF8ePHi46iWMtvXi46gk0IKZhT+k4RcVjF02g0mDhxIsxmM/Ly8kTHIaI2GAwG5OTkYPTo0QgJ4TrZlqZ/M11uq/1ykmZCCubKW1fKbZ6va6lbt25ITU3FgQMHOGOWSOEOHDgAf39/XHnllaKjKM6P2T+KjmBzQgqm5beNuIVxIiIo2oQJE+Dh4cHVf4gUrL6+Hnl5ebjqqqvg5+cnOo5iNT7XKDqCzQib/9wzsCdOVJ7AkbNHREVQrNDQUIwePRq//vor+vTpA52O53pFO3z4MHbv3o2ioiLo9Xrcf//9iIiIEB2LBNq3bx+6du2K0aNHi46iOA/89wG5rdM6z+eXsEk/xx45Jrc5LHuxq666Cr6+vjh48KDoKIRz56piYmIwYcIE0VFIAaqrq3Hq1ClMmDABXl5ebT/AxSzevVh0BLsQVjDdNOcPHfhGoKgYiuXv74+rrroKeXl50Ov1ouO4vCFDhmDs2LHo1auX6CikAHv37kV0dDQXWW9DxVMVoiPYlNDLShIjEgEA1Y3VImMoVvPMu3379omOQh1gNBrR2NjY4g+pX3l5OUpLSzFx4kR4eHiIjqM4aR+lye1AL+fqDAldwylzTibcXz4XocnUBA8t33yWvL29MWHCBHz99deoqanhxAKV2bp1KzZt2iQ6BtnY3r170adPHyQmJoqOokjpp9IBAF19ugpOYntCC6blbFndKzpIL/Jc5oXS0tKwZcsW7N27F2PGjBEdxyVkZWXhv//9r3x71qxZ6NGjR7ufZ/To0RgxYoR8u7GxEe+++65NMpIYxcXFqK6uxqxZs+DmJnSATpFM5vOXwhU/USwwiX0IXyX4n5P+ib+u/avoGIrl4eGBSZMmYenSpSgqKkJUVJToSE4vLi4O0dHR8u2O9uzd3d25ELcTMRqNyMjIwMCBAxEfHy86jiI1jxgCzrNYgSXhX5EeHf6o3M4uyxaYRLmSkpIwdOhQ7Nq1CwaDQXQcp+fp6Yng4GD5D89TEXBuKNbLywvTp0+HRqMRHUfRFl27SHQEuxBeMC31X6T+7V/sQaPRYPr06fD390dmZqboOA0cWVEAAB/BSURBVC5Jr9ejpKQEpaWlAICysjKUlJSgtrZWcDJyhDNnziA/Px9TpkxB167Od27OFnLLc+X2gykPCkxiP4oomOVPlouOoHiBgYGYNm0aiouLUVRUJDqOy8nJycHixYvx5ZdfAgB++OEHLF68mF9gXIDRaMTOnTsxcODAFuekqSVXWLVNESdYgr2D5fbEzyZi3e3rBKZRruTkZBw4cAC7du3ClClTuAKQAyUmJnJWpItqHoqdMWMGJ/pYIeuBLNER7EYx//q+Ol8AwPq89YKTKBeHZokc68yZMzh58iSHYtsw4dPzK2ANCh8kMIl9KaZgVj5VKbfP1J0RmETZODRL5BjNQ7EDBgzgUGwbfj3+KwDAT+fc14orpmBaTkEO/0e4wCTKl5yczFmzRHbGoVjrFFYXyu3KeZWX+U31U9S7YPefd4uOoAocmiWyLw7FWi/m3Ri5bblGuDNS1N9uaORQud31Lb5JL4dDs0T2waFY61nuNHXkYeffqlFRBRMAro+/HgBQVl8mOInyNQ/Npqenc2FvIhvZs2cPh2Kt5PbS+denT3AfgUkcQ3HvhuU3L5fbKw6vEJhE+ZqHZoODg7F582aYzWbRkYhU7dixYygsLMS0adM4FNsOf01zjeVNFVcwLZecuuHbGwQmUYfAwEDcfvvtMBqNPJ+pUOnp6Vi0aBGWLFkiOgpdRmlpKfbu3YurrroKaWlpbT/AxT3767Ny+91rXGNTAcUVTACof6Zebp+uPS0wiTrExsZixowZOHXqFI4ccf7zCGqTmpqKuXPnYs6cOaKj0CXU19dj69atGDRoEKZOncq1Yq3w2tbXREdwOEUWTG8Pb7kd8XaEwCTqkZKSgvHjx2Pfvn04c4bXsRJZy2QyYdOmTYiMjMTMmTO5w4wVtuRvkdvmF1znVJAiCyYAnPzrSbltMPFaw7ZoNBpMmTIFiYmJ2LZtGxcFJ7KCJEnYsWMHtFot7rjjDm7SbqUxy87vzetKvXHFFsyYgPPX9ni+4ikwiXpotVrcdttt6NatGzZt2gSj0Sg6EpGiHTx4EOXl5bjtttu416yVTlSekNu1T7vWF3PFFkwAyJiTIbctr/ehS+vSpQvuuOMOeHp6Ytu2bXzdiC7h1KlTyMnJwZQpUzBokPOuf2prse/Fyu0uui4CkzieogtmclSy3La83ocuLyIiAjNnzkRVVRX2798vOg6R4lRVVWHnzp1IS0vDuHHjRMdRjbP6s3K7+IligUnEUHwV+v6m7+U2e0vWS0hIwLRp03DkyBGcPHmy7QcQuQiDwYBNmzahT58+uOmmm7g4QTuEvBkityN8XW9CpuLfKTMSZsht9jLbZ+zYsRg5ciTS09Nx9uzZth9A5ORMJhM2b94sX7/s6cn5EdaqaqiS22V/c82V2FRRgdjL7BiNRoMZM2YgISEBv//+OyornXsnAaLLMZvN2LJlC0wmE2bPno3g4OC2H0SywDcC5XaIT8hlftN5qaJgspfZcTqdDnfddRf69OmDjRs3orq6WnQkIoczm83Ytm0b9Ho97rzzTvTq1Ut0JFUprSuV29XzXPczRDXVZ8+f98htk9kkMIn6+Pj44J577kFsbCx+++03XqNJLqX5Wsvq6mrccccdiI+PFx1JdcL+ESa3/Txd91pV1RTMpMgkue3+MlfiaC9fX1/cc889iI6Oxq+//oq6ujrRkYjsTpIk7Ny5ExUVFbj99tsxYMAA0ZFUJ7ssW26XPFEiMIl4qimYAHDowUNyu6axRmASdfL398d9992HyMhIFk0H4uLrYkiShPT0dJSWlmLmzJkYPHiw6Eiq1H9Rf7kd7hsuMIl4qiqY/bue/4fzX+AvMIl6BQYGYs6cOYiIiMCGDRs4POsAXHzd8Zp7lmfOnMHMmTMxdOjQth9EF1mVs0puu/K5y2aqKpgAkP/XfLl94MwBgUnUKygoCH/+858RHR2NDRs2cCIQOZXmCT5nz57F7NmzkZyc3PaDqFXXfX2d3Hblc5fNVFcwuwd0l9uDPuByVh3V3NPs2bMnfv31V15yQk7BZDJhy5Yt8gSfpKSkth9ErZq1fJbcNr3AiZaACgsm0HK/zDe2viEwibo1n9Ps3bs3fvvtNy5uQKrWvCiBXq/HXXfdxfVhO+nL/V8CADzcPOCmUWWpsDlVvgqW+2XO+3WewCTq5+vri/vuuw/x8fH47bffuIweqZJer8e6devQ1NSEe+65BwkJCaIjqZpm/vktuxqfaxSYRFlUWTABQHrx/Io/lv+41H4+Pj647777MGrUKGRkZCArK4srKpFqlJWVYc2aNQgMDMTcuXPRr18/0ZFUrdF4vkD+4+p/uNR+l21RbcEEgEdSH5HbRjP3fuwMnU6HW2+9FTNmzMCJEyewefNm7qdJinf8+HH8/vvv6N+/Px566CF069ZNdCTV83rVS24/MfIJgUmUR9UF873J78ltj5c9BCZxDhqNBldeeSXuu+8+NDU1Ye3atbzshBRJkiTs3r0be/fuxVVXXYV7770Xfn6cxdlZK7NXyu2CxwoEJlEmVRdMADj68FG5veboGoFJnEdCQgIeeughdO3aFevXr8eZM2dERyKSGQwGbNy4EcXFxbjllltwww03wMODX5ht4fpvrpfb0f7RApMok+oLZu/g3nJ78heTBSZxLhEREZg7dy4GDRqEzZs348iRI6IjEaG6uhpr166FRqPB/fffj1GjRvEcm41YzgUxv2AWmES5VF8wgZb/uJwAZDtdunTB3XffjYkTJ+LAgQNIT0+H2cz/SCRGUVER1q9fj+joaDz88MPo27ev6EhOw3Kvy/8b8X/8EnIJTlEwNRoNnh/zvHy7vL5cYBrnotVqMXXqVMyaNQvl5eX49ddf0djIaebkOJIk4dChQ9i+fTtSUlLwwAMPIDQ0VHQsp2K51+VbE98SmETZNJITXT9g2bu0vOyEbOP48eP47LPPcPbsWaSkpHBGopXS09ORkZEBSZJQXl6OefPmwdPTU3QsVdDr9di1axeqqqpwzTXX4Oqrr4abm1N8z1eMSZ9Pwrpj6wAAZX8rc9nNoa3hVAWzurEaAQsCAAD9Q/vj0NxDbTyC2quyshIrVqzAnj17EBkZieTkZOh0OtGxVKGxsRELFixgwbSCJEk4ceIE9u7di65du2LGjBlcjMAOzJIZ2pe08m12NC7PqTaW9Pf0Rze/bjhVcwqHyw7DYDJAp+WHuS0FBgbirrvuwsCBA7Fq1SqsXr2avU2yqeZeZWVlJUaNGoU//elP6NKli+hYTonFsn2cqmACQOHjhfLQrOcrnnwT2IFGo0FKSgr69u2LFStWYOfOnextUqdd2KucM2cON3y2o4dXPyy3y5/kvA9rOOXJgMqnzu+8MeTDIQKTOLfm3uYdd9wBvV6P1atX49SpU6JjkQrp9Xps2rQJ+/btw6hRo/D444+zWNqRWTJjYcZC+Xawd7DANOrhdD1MAAjwCsDg8MHIOp2FrNNZ0DfpWyzYTrbD3iZ1BnuVYnAotmOcsocJAPse2Ce3fV7zEZjENbC3Se1l2ascOXIke5UOcsM3N8hty5XSqG1O2cNsVjWvSp41q5mv4TcpO2utt9m1a1ckJSVxnU+SmUwm5OTkIDs7m71KB6tvqseK7BXybcuV0qhtTl0w/T39Man3JKw9thYAcKT8CPqGcHUQe2vubQ4ZMgRr167F2rVrER0djSFDhsDbm0PjrspsNiMvLw8HDhyAh4cHxo8fjwkTJnAGrAN1ee38a80ORPs51XWYl8IFDcRpamrCrl27sGHDBpSXl6NXr14YMGCAS57fdNXrMCVJQkFBAbKysmA2m5GSkoIJEyaga9euoqO5FMvPwYqnKhDoFXiZ36bWOHUPs1nT803y9l8cmnUsDw8PjP7/7d17dNP13Qfwdy69pOklpS21ScullbYKVC5W4QjoYMrmUR4vK+qZm4+gsD1zOgUFtFAo1jEd4plP3XnAy5xUeE45OypsIOOhjGKnDLlVoG3KxaZXSFvStEmb2+/5gxGaXmha2vx+Sd6vc3oO32/S8KGkeef7/X3z/c6ahenTp+PQoUMoKSnBrl27kJGRgczMTCgUioEfhPxWU1MTjh07hs7OTmRlZeG+++5DcjJPwfC1b2q/cf958dTFDMshUqxdu3at2EWMNLlMjtu1t2Pbd9sAAFa7Ffem3StyVcElJCQEaWlpyM7OhlwuR3l5Oc6cOQOlUgmNRhMUmz07nU4cOnQIs2bNglIZ2O9VW1paUFZWBr1ej7S0NDzxxBOYO3cuYmJixC4t6AiCgJR3Utzto0uPiliNfwuKKdmruk9JmFeZERkaKWI1wc1oNGLfvn04fPgw5HI5srKykJKSEtDBGQxTsu3t7Th27BguXryIcePGYf78+Zg4cWJA/79KXc9ju/h/MXRBFZgAr2dKTV1dHfbu3YsTJ04gNDQUGRkZGDduXEBN1QbD5uvNzc04c+YMGhsbodVqce+992LatGkB9f/oj0LWh8DhcgAATv7iJCYnTha5Iv8WdIHZYetA5G+vjSwZmuITBAHnzp1DaWkpysvLYbfbMXbsWGRkZCAyMnBmAQJthOl0OnH+/Hno9XpYrVbodDrcdddduOOOO4JyUZfUHKo5hNkfzQYApMam4uzzZ0WuyP8F9oWUPqhD1fj4oY/x1GdPAQAe2v4QPnv8M5GrCm4ymQxpaWlIS0uD0WjEkSNH8PXXX2PPnj2IjY1FRkYGdDodp5Ikwmw2o7KyEjU1NQgJCUFWVhbuvPNOpKen8+gtiXC4HO6wBMCwHCZBN8K8qvvUbMWvKpARnyFiNdSTzWbDd999h7KyMpw9e+WXPTU1FRMmTEB4eLjI1Q2NP48wXS4X6urqUFVVhdbWViQkJGDGjBm4/fbbERfH8xOlhtctR0bQjTCvEvIE95MqszATzjVOyGV8dywVoaGhmDZtGqZOnYq6ujr3dcDKykokJiYiMzMT8fHxfCEYYVarFdXV1Th79ixkMhnS09PxyCOPYNKkSQgJCRG7POpD97Csf6mevyPDKGgDE7jyzkuefyUkFfkKXs+UIJlMhuTkZCQnJ2P+/Pk4fvw4ysrKUFpaitDQUGi1WqSkpDA8h5HFYoHBYEBtbS1aW1sRHR2Nu+++G3fccQfPPZW4Ge/PcP/5t/N+i6SoJBGrCTxBOyV7VY2pBmPfGetuMzSlz+Vy4ezZsygvL0d5eTlaWloAAImJiUhJSUFSUpIkP+co1SlZQRDQ2toKg8GA+vp6tLe3Q61WIz09HZMmTUJWVhYiIniAgdSVnC/B3D/Pdbf5Wjb8gj4wAeDNr97Ein0rAADxEfG49PIlkSsib7lcLhgMBlRWVqK8vBx1dXWw2WwYNWoUkpOTkZKSIpn9a6UUmE6nE42NjTAYDGhqaoLT6YRGo8GkSZOQmZmJm2++mSHpR6x2q8epTAzLkcHA/Lfu8/5bHtyCZ6Y9I2I1NBRXP+dYWVmJ06dPQ6/Xw2KxQK1WQ6fTITk5GRqNRrSVnGIHptVqRX19PWpra2E0GqFUKnHTTTdh8uTJyMjIwNixYyU5MqeBcZGPbzAwu+n+pDO8aEByNPe89GcdHR3Q6/WoqKjAqVOnYDKZIAgCIiMjERsbi7i4OMTFxSE6Ovq6Iep0OlFSUgK9Xo/W1laEhYUhNTUVP/zhDwd1bJkvA9NqtaKlpQVGoxEtLS1oa2uDzWaDSqVCWloabr31VmRkZCAxMZEvrn6u++uWfbUdSjnf9IwU/mS76b5yNmVTChyrHVDIuVOJv1Kr1ZgyZQqmTJkCh8OBmpoa1NfXo76+Ht9//z3OnDkDm802YIja7XY0NDRgzpw5SExMRGdnJ/bs2YNt27ZhyZIlIv8r+w/HsLAwREdHY9y4cdDpdNBqtRgzZgyio6PFLpmGSfew1P9az7AcYfzp9tB95axyvZLXAgKEUqlEamoqUlNT3X1WqxUNDQ1oaGhAXV1dnyEaHR2NiIgIzJgxAyqVCnK5HHFxcfjRj36EDz74ACaTacQ3FLfb7bBYLLBarbBarbBYLLBYLGhvb+8zHJOTk5GUlAStVovY2FiOIANU97DMvycfN4+6WcRqggMDsweZTAbTShNiNlx5EeRxYIFLpVINGKKNjY0wmUyora2F0+l0fzU2NqK6uhoHDx6EWq2GSqWCSqVCREQEwsLCIJPJ4HK5AFx5TsnlctjtdnR2dqKpqQlKpRKCIMDlckEQBDgcDncQWq1WdHV1oaurCzabDS6XCwqFwv0VHh4OjUaD8ePHQ6fTMRyD0OLPF3u0V9+9WqRKgguvYfbjSP0RZG/JdrcZmsHN6XSivb0dZrMZzc3NePzxx6HT6fD888/DZDLBZDLh8uXLMJvNcDiubHb97bff4ujRK0cpdQ+yn/3sZ+69Vq/2y2QyREREICYmBhqNBhqNBpGRkYiKinJ/XW2HhoYyGIPYjtM7kFOc427ztcl3GJjXsbFsI5b/fbm7zSdmcCgqKsLSpUvd7d27d2P27Cv7ctrtduTk5KCmpgYHDhzodT3Q6XSiq6sLLpfLPYV6dRRpMpkwdepUnD9/HjExMVAoFJDL5ZDL5VAqldywnAZ0+tJpTHxvorvN1yTfYmAOYO7Hc1FyocTd5hM08JnNZjQ1NbnbOp0OKpUKdrsdCxcuxLlz57B///5B76Ha1taGmJgYmEwmLryhQTNajEh4K8Hd5muR7zEwvdD94nq2NhuHnz0sYjUkhqthqdfrUVJSgoSEhIG/qQcGJg1Vz40JuPe1OPgT90L3d3L/qv8XFn2+SMRqyNccDgd+8pOf4MiRIygqKnIv+mlsbITNZhO7PApwDpfDIyxtuTaGpUg4whyE7iPN12a/htfnvi5iNeQrFy5cwPjx4/u8raSkBPfcc49Xj8MRJg2W0+WEcv21DzO0r2qHOlQtYkXBjYE5SN1Dc8O8DVgxa4WI1ZA/YWDSYLgEFxT51zZOaXmlBbGqWBErIo7rB6n79OzK/1uJt756S8RqiCgQMSyliYE5BN1D85V9ryD/H/kiVkNEgaRnWNa+WMuwlAgG5hB1D828A3l4YfcLIlZDRIHA6XJ6hKXhRQN00Ty0WyoYmDege2j+4fAfsGDbAhGrISJ/1uXo8ljgU/9SPU9MkhgG5g3qHpo7q3ZCu1ErYjVE5I8ud15GeEG4u938SjOSopJErIj6wsAcBt1Ds6G9wWMlLRHR9ZxrPYfY3127RmnLtWGUapSIFVF/GJjDpOc2VQxNIhrI/vP7kfaHNHfbucaJEEWIiBXR9TAwh5GQJyA19tpRUQxNAoDCwkLceuutyM7OHvjOFDQ2lm3EvD/Pc7cdqx3cwUfiuHHBCHj2i2fx/rH33W1ukkwANy6ga2Z/NBuHag652641Lh7Z5gf4dmYEbFmwBe/d/567LVsng9PlFLEiIpIK2TqZR1gKeQLD0k8wMEfIL7N/ibJFZe62cr0SDeYGESsiIrH1vEzD2Sf/wsAcQTNTZuLi8ovutvZtLYpPFYtYERGJQRAEj7CckTyDYemHGJgjLEGdAMdqh7u9cMdCZP0xS8SKiMiXWqwtkOdfe6nd/MBm/HPxP0WsiIaKgekDCrnC491k+cVyrqAlCgJbT25F3Jtx7rb+13o8O/1ZESuiG8FVsj7WMyi5Oi54cJVscOn5u96V24VQRahI1dBw4AjTx4Q8Aa//4NrB0/J8OSqNlSJWRETDra/FPQxL/8fAFMFrc17DhRcuuNuZhZm4v+h+8QoiomHRam31CMsxMWO4uCeAMDBFMlYzFq41Lnd7d/VuXtck8mO5+3Mx6s1re8DufXIvvv/N9yJWRMON1zAloGdQtq5ohSZcI1I1NFJ4DTNw9fwdbl/VDnWoWqRqaKRwhCkBQp6ArQ9vdbdjfxeLpz9/WsSKiMgbVru1z+uVDMvAxMCUiJ9m/RTtq9rd7T8d/xOnaAMEN18PTMu+XIaINyLc7aJHini9MsBxSlaCegZlxa8qkBGfIVI1NFw4JRs4+JGR4MQRpgQJeQK+XfKtu51ZmMnRJpEEnLp4ih8ZCWIcYUqY0+WEcr3So6/j1Q5EhET08x0kZRxh+reeQfmXhX/Bw7c8LFI1JAaOMCXs6pZ688ZfO2RW/YYa87fOF7EqouDSbGnuFZaO1Q6GZRDiCNNPNFuaEf9WvEefLdeGEEWISBXRYHGE6X96BuVz2c/h3fvfFakaEhsD088o8hVwCdc2PLhn3D0oeapExIrIWwxM/9HY3oikjUkeffxsJTEw/dCljksY/fvRHn2XV1xGTHiMSBWRNxiY/qHnqHJ+2nzseXKPSNWQlDAw/Zj6DTUsdotHHz8HJl0MTGn7a9Vf8cC2Bzz6LK9aoApRiVQRSQ0X/fixjlc70LayzaNPtk6GLyq/EKkiIv/jElyQrZN5hOXb970NIU9gWJIHjjADRP4/8pF3IM+jj4uCpIUjTOnp6/PNjtUOKOQKEaohqWNgBhCX4IIiv/cvOqdppYGBKR07K3diwfYFHn0nf3ESkxMni1QR+QNOyQYQuUwOIU9A1XNVHv2ydTK8vPdlkaoiko52Wztk62QeYfnYxMcg5AkMSxoQR5gB7PWDr2N1yWqPvuNLj+O2m24TqaLgVFhYiMLCQjidTlRVVXGEKQJBECDP7z0+cK1xQSbjtpPkHQZmEOjrOk3byjZEhUWJUE3w4pSsOPp6/vPMWRoKTskGASFPgGO1w6MvekM0ZOtkcLqcIlVFNLJyinN6heUXj38BIU9gWNKQcIQZZGrbapGyKaVXP6emRh5HmL6x/h/rsebAGo++J7OexCcPfyJSRRQoGJhB6uvarzHzg5m9+hmcI4eBObLe/ufbWLZ3mUdffEQ8Lr18SaSKKNAwMIPcbv1u3P/p/b36GZzDj4E5MlbtW4UNX23o1c/nMA03BiYBAD458Ql+/tnPe/XzJPnhw8AcXnM+moPSmtJe/c41TshlXJ5Bw4+BSR52nN6BnOKcXv01v6lBSkzva5/kPQbm8Ohr1SvAESWNPAYm9elow1FM3zy9V//7D76PxdMWi1CR/2NgDp3VbkXEGxG9+sfEjMGFFy4wKMknGJh0XTWmGox9Z2yft3HLvcFhYA5ef9fYc2fnYv3c9SJURMGMgUle6XR0QlXQ98kNjcsakRiZ6OOK/A8D03v9TbtWPleJ9Lh0H1dDdAUDkwZtxd9X4M2yN3v1//jmH+NvP/2bCBX5Bwbm9VUaK5FZmNnnbTx5h6SAgUlDZjAZMOadMX3eVv3raqSNSvNxRdLGwOytvz1eAeCB9Aew84mdPq6IqH8MTLphTpcTyvXKfm8P9vMFufl6b30dDHAV32yRVDEwaVhVGCtwS+Etfd6mjdKi9sXaoF3RGOwjzF1Vu/Dgtgf7vO3pKU/jw//40McVEQ0OA5NGhCAIyDuQh/UH+17JmKhORMOyhqAKz2AMzOJTxVi4Y2G/t5tXmREZGunDioiGjoFJI87pcmLyHyfjjPFMv/exvmZFuDLch1X5XrAE5ktfvoRNX2/q9/ZLL19CfES8DysiGh4MTPIpl+DChHcn4FzruX7vc+CpA7h73N0+rMo3AjUwuxxdCC+4/pudil9VICM+w0cVEY0MBiaJxuFyYMnOJfjo+EfXvZ/lVQtUIX1/BtSfBFJgbizbiOV/X37d+/CQZgo0DEySDH2zHun/ff0Ppd+WeBuOLDkCpbz/VblS5c+B+XnF53jofx+67n0em/gYih4pCuoV0RTYGJgkSeYuM2Z9NAsnm04OeN+6l+qgjdL6oKob4y+B6XQ58dRnT6GovGjA+x559gima3vvOUwUiBiY5BfqzfXQva3z6r7aKC1O/dcpyU0HSjEwBUHAG6VvILck16v7b390OxZOXBhUq5uJrmJgkl8yWoyY9j/TYGgzeP09mx/YjGemPTOkF/u1a9di+/btMBgMCA0NxfTp01FQUIA777zT68cQOzCrW6ox4d0Jg/qeg/95ELPGzGJAEoGBSQGkzFCGuz68a9DfpwnX4Msnv0S2NrvfYPj0008xevRopKamwmq1YtOmTSguLkZ1dTUSEhK8+nt8EZhtXW3I3Z+Ldw+/O+jvXT5zOdb9YB0iQnofo0VEDEwKYIIgwNBmwLK9y7Dj9I4beqyo0CjkzsnFE5OeQHJ0MsxmM2JiYrBv3z7MmzfPq8e4kcC02q3YVbULBaUFONF0Yij/BA8nfnECWYlZN/w4RMGEgUlBqbqlGm999RY2H93su7+0E8AGACsB+GCPhtHq0SjOKcbM5Jk86YNoGDAwiXqwOW2oaq7C9u+2o6C0YPgeeJgD89FbHsXKWSuRGZ8JdYia1xmJRpj/fZiNaIQVby/G0qVLAQBqqLF7927Mnj0bHR0daGhogNFoxJYtW7B//3588803GD16NARBQLO1GRc7LqLGVAOjxYitf9mKL/d/CYQCiADw77emi6YuQlxsHJKjk5ESnQJNuAaacA1GqUYhQZ0AlVLF8COSII4wiXowm81oampyt3U6HVSq3jsNTZgwAYsWLcKqVav6fJyuri50dXW5221tbUhJSZHUx0qIyHscYRL1EBUVhaioqAHvJwiCRyD2FBYWhrCwsOEsjYhExMAkGkBHRwcKCgqwYMECJCUlobm5Ge+99x5qa2uRk5MjdnlE5CMMTKIBKBQKVFRU4OOPP4bRaERcXByys7NRWlqKiRMnil0eEfkIr2ES+YjYO/0Q0Y2Ri10AERGRP2BgEhEReYGBSURE5AVewyTyEUEQYDabERUVxY0JiPwQA5OIiMgLnJIlIiLyAgOTiIjICwxMIiIiLzAwiYiIvMDAJCIi8gIDk4iIyAsMTCIiIi8wMImIiLzAwCQiIvICA5OIiMgL/w+pXLtsaSua9gAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = circle((0, 0), 2*m, edgecolor='black', fill=True, facecolor='grey', alpha=0.5)\n", "graph += geod.plot_integrated(chart=Xcart, ambient_coords=(x,y), plot_points=500, \n", " aspect_ratio=1, color='green') \n", "graph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Other null geodesics" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "U(r) = (1 - 2/r)/r^2" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "b = 7.07106781186548 m\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "v_0 = 5/4 d/dt - 0.774596669241483 d/dr + 0.0707106781186548 d/dph" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U1 = 0.02\n", "b = 1/sqrt(U1)\n", "print(\"b = {} m\".format(b))\n", "r0 = 10\n", "v0 = initial_vector(r0, b, inward=True)\n", "v0.display()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 7 graphics primitives" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "geod = M.integrated_geodesic(g, (s, 0, 50), v0)\n", "sol = geod.solve(step=0.01, method=\"ode_int\") \n", "interp = geod.interpolate() \n", "graph += geod.plot_integrated(chart=Xcart, ambient_coords=(x,y), plot_points=500, \n", " aspect_ratio=1, color='red', thickness=1.5,\n", " display_tangent=True, color_tangent='red', \n", " plot_points_tangent=4, scale=1) \n", "graph" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "b = 5.00000000000000 m\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "v_0 = 5/4 d/dt - 0.894427190999916 d/dr + 0.0500000000000000 d/dph" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U1 = 0.04\n", "b = 1/sqrt(U1)\n", "print(\"b = {} m\".format(b))\n", "r0 = 10\n", "v0 = initial_vector(r0, b, inward=True)\n", "v0.display()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0.000000000000000" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p0 = v0.parent().base_point()\n", "g.at(p0)(v0, v0)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 11 graphics primitives" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "geod = M.integrated_geodesic(g, (s, 0, 13.25), v0)\n", "sol = geod.solve(step=0.001, method=\"ode_int\") \n", "interp = geod.interpolate() \n", "graph += geod.plot_integrated(chart=Xcart, ambient_coords=(x,y), plot_points=500, \n", " aspect_ratio=1, color='brown', thickness=1.5,\n", " display_tangent=True, color_tangent='brown', \n", " plot_points_tangent=3, scale=0.2) \n", "graph" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 11 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph, xmin=-10)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "b = 4.66252404120157 m\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "v_0 = 21.0000000000000 d/dt + 0.874792273707413 d/dr + 1.05726168734729 d/dph" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U1 = 0.046\n", "b = 1/sqrt(U1)\n", "print(\"b = {} m\".format(b))\n", "r0 = 2.1\n", "v0 = initial_vector(r0, b)\n", "v0.display()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4.440892098500626e-15" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p0 = v0.parent().base_point()\n", "g.at(p0)(v0, v0)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 15 graphics primitives" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "geod = M.integrated_geodesic(g, (s, 0, 20), v0)\n", "sol = geod.solve(step=0.001, method=\"ode_int\") \n", "interp = geod.interpolate() \n", "graph += geod.plot_integrated(chart=Xcart, ambient_coords=(x,y), plot_points=500, \n", " aspect_ratio=1, color='orange', thickness=1.5,\n", " display_tangent=True, color_tangent='orange', \n", " plot_points_tangent=3, scale=0.1) \n", "graph" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 15 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph, xmin=-10)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "b = 5.34522483824849 m\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "v_0 = 6.00000000000000 d/dt + 0.416269652125186 d/dr + 0.927990423307029 d/dph" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U1 = 0.035\n", "b = 1/sqrt(U1)\n", "print(\"b = {} m\".format(b))\n", "r0 = 2.4\n", "v0 = initial_vector(r0, b, ph0=-pi/2)\n", "v0.display()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 19 graphics primitives" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "geod = M.integrated_geodesic(g, (s, 0, 3.5), v0)\n", "sol = geod.solve(step=0.001, method=\"ode_int\") \n", "interp = geod.interpolate() \n", "graph += geod.plot_integrated(chart=Xcart, ambient_coords=(x,y), plot_points=500, \n", " aspect_ratio=1, color='grey', thickness=1.5,\n", " display_tangent=True, color_tangent='grey', \n", " plot_points_tangent=3, scale=0.1) \n", "graph" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "graph += text('1', (5, 4.5), color='red' ) \\\n", " + text('2', (3, 3.8), color='brown' ) \\\n", " + text('3', (-6, 3.5), color='orange' ) \\\n", " + text('4', (0.7, -2.7), color='grey' )" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 23 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph, xmin=-10, ymin=-4, axes_labels=[r'$x/m$', r'$y/m$'])" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "graph.save(\"ges_null_geod.pdf\", xmin=-10, ymin=-4, axes_labels=[r'$x/m$', r'$y/m$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geodesics arising from a source at large distance" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "r0 = 100 # distance of the source" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "b_sel = [12., 8., 6., 5.355, 5.23, 5.2025, 5.19643, 5.196155]\n", "#b_sel = [15., 10., 7., 6., 5.5, 5.23, 5.22, 5.2025, 5.198, 5.197, 5.1965, 5.19632]\n", "b_pec = [5.355, 5.2025, 5.19632, 5.196155]" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "b = 12.000000 m\n", "s=0: (0.0, 100.0, 1.5707963267948966, 0.12028988239478806)\n", "s=150: (161.7386305994338, 49.599207321700575, 1.5707963267948966, 3.3499140843834243)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "b = 8.000000 m\n", "s=0: (0.0, 100.0, 1.5707963267948966, 0.08008558003365901)\n", "s=150: (165.0262559276518, 47.87567237981162, 1.5707963267948966, 3.832461957010324)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "b = 6.000000 m\n", "s=0: (0.0, 100.0, 1.5707963267948966, 0.06003605844527842)\n", "s=150: (169.51340790400954, 46.21354032584246, 1.5707963267948966, 4.730793903988559)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "b = 5.355000 m\n", "s=0: (0.0, 100.0, 1.5707963267948966, 0.05357562643499787)\n", "s=150: (175.13467942245063, 43.837643428812676, 1.5707963267948966, 6.172293011040655)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "b = 5.230000 m\n", "s=0: (0.0, 100.0, 1.5707963267948966, 0.052323872006442895)\n", "s=150: (180.39625091484754, 41.32000814165003, 1.5707963267948966, 7.665165130714838)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "b = 5.202500 m\n", "s=0: (0.0, 100.0, 1.5707963267948966, 0.052048497112969744)\n", "s=150: (186.05222271416335, 38.48872884422706, 1.5707963267948966, 9.317135314376204)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "b = 5.196430 m\n", "s=0: (0.0, 100.0, 1.5707963267948966, 0.05198771489670833)\n", "s=150: (196.57550821738923, 33.13574656928606, 1.5707963267948966, 12.42140053051524)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "b = 5.196155 m\n", "s=0: (0.0, 100.0, 1.5707963267948966, 0.05198496117647258)\n", "s=150: (212.1623795944796, 25.165821003889214, 1.5707963267948966, 17.043633460770014)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#b_sel = [5.19643]\n", "for b in b_sel:\n", " print('b = {:.6f} m'.format(float(b)))\n", " graph = circle((0, 0), 2*m, edgecolor='black', fill=True, facecolor='grey', alpha=0.5)\n", " graph += circle((0, 0), 3*m, color='lightgreen', thickness=1., linestyle='--', zorder=1)\n", " graph += text(r'$b = {:.6f} \\, m$'.format(float(b)), (-8, 12), fontsize=14, \n", " color='black')\n", " ph0 = asin(b/r0)\n", " v0 = initial_vector(r0, b, ph0=ph0, inward=True)\n", " geod = M.integrated_geodesic(g, (s, 0, 150), v0)\n", " sol = geod.solve(step=0.001, method=\"odeint\", rtol=1.e-12, atol=1.e-12) \n", " interp = geod.interpolate()\n", " first_point = geod(0)\n", " print(\"s=0: {}\".format(first_point.coord()))\n", " last_point = geod(150)\n", " print(\"s=150: {}\".format(last_point.coord()))\n", " graph += geod.plot_integrated(chart=Xcart, ambient_coords=(x,y), plot_points=500, \n", " aspect_ratio=1, color='green', thickness=1.5, zorder=2,\n", " display_tangent=True, color_tangent='green', \n", " plot_points_tangent=12, scale=0.1) \n", " show(graph, xmin=-12, xmax=12, ymin=-12, ymax=12, axes_labels=[r'$x/m$', r'$y/m$'])\n", " filename = 'ges_null_b_{:.6f}'.format(float(b))\n", " filename = filename.replace('.', '_') + '.pdf'\n", " graph.save(filename, xmin=-12, xmax=12, ymin=-12, ymax=12, axes_labels=[r'$x/m$', r'$y/m$'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Check of the law $b - b_{\\rm crit} \\sim 648(7\\sqrt{3} - 12) m \\, \\mathrm{e}^{-\\Delta\\varphi}$" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "b_c = n(3*sqrt(3))\n", "a = n(648*(7*sqrt(3) - 12))" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0.0338475772933684, 0.0398130627050151, 0.149837390201463)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = 5.230000\n", "Dphi = 7.665165130714838 - 0.052323872006442895\n", "b - b_c, a*exp(-Dphi), abs((b - b_c)/(a*exp(-Dphi)) - 1)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0.00634757729336766, 0.00762894456367238, 0.167961276898820)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = 5.202500\n", "Dphi = 9.317135314376204 - 0.052048497112969744\n", "b - b_c, a*exp(-Dphi), abs((b - b_c)/(a*exp(-Dphi)) - 1)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0.000277577293368303, 0.000342194329014259, 0.188831404167611)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = 5.196430\n", "Dphi = 12.42140053051524 - 0.05198771489670833\n", "b - b_c, a*exp(-Dphi), abs((b - b_c)/(a*exp(-Dphi)) - 1)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(2.57729336805568e-6, 3.36404158971445e-6, 0.233869945028104)" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = 5.196155\n", "Dphi = 17.043633460770014 - 0.05198496117647258\n", "b - b_c, a*exp(-Dphi), abs((b - b_c)/(a*exp(-Dphi)) - 1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.1.beta0", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }