{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Allgemeine Relativitätstheorie mit dem Computer \n",
    "# General Theory of Relativity on the Computer\n",
    "\n",
    "## Vorlesung gehalten an der J.W.Goethe-Universität in Frankfurt am Main (Wintersemester 2026/27)\n",
    "\n",
    "### von Dr.phil.nat. Dr.rer.pol. Matthias Hanauske\n",
    "\n",
    "### Frankfurt am Main 23.09.2026\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bewegung eines Probekörpers um ein nicht-rotierendes schwarzes Loch in der Ebene \n",
    "## Teil I: Radialer Fall eines Probekörpers  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Im Folgenden wird die Geodätengleichung in vorgegebener Schwarzschild Raumzeit betrachtet. Die Geodätengleichung beschreibt wie sich ein Probekörper (Masse Probekörper $m << M$ Masse schwarzes Loch) im Raum bewegt und sagt voraus, dass diese Bewegung sich stets entlang der kürzesten Kurve, in der durch die Metrik beschriebenen gekrümmten Raumzeit, vollzieht. Zunächst wird das Python-Modul \"OGRePy\" eingebunden, welches auf dem Modul SymPy basiert und symbolische Berechnungen in der Allgemeinen Relativitätstheorie relativ einfach möglich macht. Eine ausführliche Einführung in das Modul \"OGRePy\" finden sie unter dem folgenden Link: <A href=\"https://github.com/bshoshany/OGRePy/blob/master/OGRePy/docs/OGRePy_Documentation.ipynb\" target=\"_blank\">OGRePy-Documentation</A>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definition der Koordinaten und der kovarianten Raumzeit-Metrik der Schwarzschildmetrik:\n",
    "$$ g_{\\mu\\nu}=\\left( \\begin{array}{ccc} 1-\\frac{2\\,M}{r} & 0 & 0 & 0\\\\ 0&  -\\frac{1}{1-\\frac{2\\,M}{r}}&  0&0 \\\\ 0&  0&  -r^2& 0\\\\ 0&  0&  0& -r^2 \\hbox{sin}^2(\\theta)\\end{array} \\right)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "<b>\n",
       "OGRePy: An <u>O</u>bject-Oriented <u>G</u>eneral <u>Re</u>lativity Package for <u>Py</u>thon<br />\n",
       "By <a href=\"https://github.com/bshoshany\">Barak Shoshany</a> (<a href=\"mailto:baraksh@gmail.com\">baraksh@gmail.com</a>) (<a href=\"https://baraksh.com/\">baraksh.com</a>)<br />\n",
       "v2.0.0 (2026-05-11)<br />\n",
       "GitHub repository: <a href=\"https://github.com/bshoshany/OGRePy\">https://github.com/bshoshany/OGRePy</a><br />\n",
       "Documentation: <a href=\"/home/hanauske/neu_2026/VARTC_2026/ART_env/lib/python3.14/site-packages/OGRePy/docs/OGRePy_Documentation.ipynb\">.ipynb</a>, <a href=\"/home/hanauske/neu_2026/VARTC_2026/ART_env/lib/python3.14/site-packages/OGRePy/docs/OGRePy_Documentation.pdf\">.pdf</a>, <a href=\"#\" onclick=\"window.open('file:///home/hanauske/neu_2026/VARTC_2026/ART_env/lib/python3.14/site-packages/OGRePy/docs/OGRePy_Documentation.html', '_blank')\">.html</a>\n",
       "</b>"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import OGRePy as gr\n",
    "from sympy import *\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Um symbolische Rechnungen in einer gekrümmten Raumzeit machen zu können, müssen wir zunächst wieder das verwendete Koordinatensystem und die gekrümmte Metrik der Raumzeit (hier die Schwarzschild-Metrik) definieren."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from OGRePy.abc import t, phi, theta\n",
    "r = gr.sym(\"r\", nonnegative=True)\n",
    "M = gr.sym(\"M\", nonnegative=True)\n",
    "\n",
    "Spherical = gr.Coordinates(t, r, theta, phi)\n",
    "\n",
    "g = gr.Metric(\n",
    "    coords = Spherical,\n",
    "    components = gr.diag((1-2*M/r), -1/(1-2*M/r), -r**2, -r**2*gr.s.sin(theta)**2),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$$g{}_{\\mu}{}_{\\nu}\\Bigg|_{\\left(t, r, \\theta, \\phi\\right)} = \\left(\\begin{matrix}- \\frac{2 M}{r} + 1 & 0 & 0 & 0\\\\0 & - \\frac{1}{- \\frac{2 M}{r} + 1} & 0 & 0\\\\0 & 0 & - r^{2} & 0\\\\0 & 0 & 0 & - r^{2} \\sin^{2}{\\left(\\theta \\right)}\\end{matrix}\\right)$$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Chistoffel Symbole (zweiter Art): \n",
    "$$ \\Gamma^{\\sigma}_{\\mu \\nu} = \\frac{1}{2}g^{\\sigma \\alpha} \\left( g_{\\nu \\alpha| \\mu} + g_{\\mu \\alpha| \\nu} - g_{\\mu \\nu| \\alpha} \\right)$$\n",
    "\n",
    "Hier speziell $$ \\Gamma^{1}_{1 1} = \\Gamma^{r}_{r r}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "**OGRePy**: You have the latest version of the package."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "$$\\begin{align*}\n",
       "    \\Gamma{}_{t}{}_{t}{}^{r} &= \\frac{M \\left(2 M - r\\right)}{r^{3}} \\\\\n",
       "    \\Gamma{}_{t}{}_{r}{}^{t} &= \\frac{M}{r \\left(- 2 M + r\\right)} \\\\\n",
       "    \\Gamma{}_{r}{}_{t}{}^{t} = \\Gamma{}_{r}{}_{r}{}^{r} &= \\frac{M}{r \\left(2 M - r\\right)} \\\\\n",
       "    \\Gamma{}_{r}{}_{\\theta}{}^{\\theta} = \\Gamma{}_{r}{}_{\\phi}{}^{\\phi} = -\\Gamma{}_{\\theta}{}_{r}{}^{\\theta} = -\\Gamma{}_{\\phi}{}_{r}{}^{\\phi} &= - \\frac{1}{r} \\\\\n",
       "    \\Gamma{}_{\\theta}{}_{\\theta}{}^{r} &= - 2 M + r \\\\\n",
       "    \\Gamma{}_{\\theta}{}_{\\phi}{}^{\\phi} = -\\Gamma{}_{\\phi}{}_{\\theta}{}^{\\phi} &= - \\frac{1}{\\tan{\\left(\\theta \\right)}} \\\\\n",
       "    \\Gamma{}_{\\phi}{}_{\\phi}{}^{r} &= \\left(- 2 M + r\\right) \\sin^{2}{\\left(\\theta \\right)} \\\\\n",
       "    \\Gamma{}_{\\phi}{}_{\\phi}{}^{\\theta} &= \\frac{\\sin{\\left(2 \\theta \\right)}}{2} \n",
       "\\end{align*}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g.christoffel().list(indices=(-1,-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{M}{r \\left(2 M - r\\right)}$"
      ],
      "text/plain": [
       "     M     \n",
       "───────────\n",
       "r⋅(2⋅M - r)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.christoffel().components(indices=(-1,-1,1),coords=Spherical)[1,1,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Riemann Tensor:\n",
    "$$ R^{\\mu}{}\\!_{\\nu \\rho \\sigma} = \\frac{\\partial \\Gamma^{\\mu}_{\\nu \\sigma}}{\\partial x^{\\rho}} - \\frac{\\partial \\Gamma^{\\mu}_{\\nu \\rho}}{\\partial x^{\\sigma}} + \\Gamma^{\\alpha}_{\\nu \\sigma}\\Gamma^{\\mu}_{\\rho \\alpha} - \\Gamma^{\\alpha}_{\\nu \\rho}\\Gamma^{\\mu}_{\\sigma \\alpha} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$$\\begin{align*}\n",
       "    R{}^{t}{}_{r}{}_{t}{}_{r} = -R{}^{t}{}_{r}{}_{r}{}_{t} &= \\frac{2 M}{r^{2} \\left(- 2 M + r\\right)} \\\\\n",
       "    R{}^{t}{}_{\\theta}{}_{t}{}_{\\theta} = -R{}^{t}{}_{\\theta}{}_{\\theta}{}_{t} = R{}^{r}{}_{\\theta}{}_{r}{}_{\\theta} = -R{}^{r}{}_{\\theta}{}_{\\theta}{}_{r} &= - \\frac{M}{r} \\\\\n",
       "    R{}^{t}{}_{\\phi}{}_{t}{}_{\\phi} = -R{}^{t}{}_{\\phi}{}_{\\phi}{}_{t} = R{}^{r}{}_{\\phi}{}_{r}{}_{\\phi} = -R{}^{r}{}_{\\phi}{}_{\\phi}{}_{r} &= - \\frac{M \\sin^{2}{\\left(\\theta \\right)}}{r} \\\\\n",
       "    R{}^{r}{}_{t}{}_{t}{}_{r} = -R{}^{r}{}_{t}{}_{r}{}_{t} &= \\frac{2 M \\left(- 2 M + r\\right)}{r^{4}} \\\\\n",
       "    R{}^{\\theta}{}_{t}{}_{t}{}_{\\theta} = -R{}^{\\theta}{}_{t}{}_{\\theta}{}_{t} = R{}^{\\phi}{}_{t}{}_{t}{}_{\\phi} = -R{}^{\\phi}{}_{t}{}_{\\phi}{}_{t} &= \\frac{M \\left(2 M - r\\right)}{r^{4}} \\\\\n",
       "    R{}^{\\theta}{}_{r}{}_{r}{}_{\\theta} = -R{}^{\\theta}{}_{r}{}_{\\theta}{}_{r} = R{}^{\\phi}{}_{r}{}_{r}{}_{\\phi} = -R{}^{\\phi}{}_{r}{}_{\\phi}{}_{r} &= \\frac{M}{r^{2} \\left(- 2 M + r\\right)} \\\\\n",
       "    R{}^{\\theta}{}_{\\phi}{}_{\\theta}{}_{\\phi} = -R{}^{\\theta}{}_{\\phi}{}_{\\phi}{}_{\\theta} &= \\frac{2 M \\sin^{2}{\\left(\\theta \\right)}}{r} \\\\\n",
       "    R{}^{\\phi}{}_{\\theta}{}_{\\theta}{}_{\\phi} = -R{}^{\\phi}{}_{\\theta}{}_{\\phi}{}_{\\theta} &= - \\frac{2 M}{r} \n",
       "\\end{align*}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g.riemann().list(exact=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Ricci Tensor:\n",
    "\n",
    "$$ R_{\\mu \\nu} = R^{\\sigma}{}\\!_{\\mu \\sigma \\nu} = \\frac{\\partial \\Gamma^{\\sigma}_{\\mu \\nu}}{\\partial x^{\\sigma}} - \\frac{\\partial \\Gamma^{\\sigma}_{\\mu \\sigma}}{\\partial x^{\\nu}} + \\Gamma^{\\rho}_{\\mu \\nu}\\Gamma^{\\sigma}_{\\rho \\sigma} - \\Gamma^{\\sigma}_{\\mu \\rho}\\Gamma^{\\rho}_{\\nu \\sigma} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$$R{}_{\\mu}{}_{\\nu}\\Bigg|_{\\left(t, r, \\theta, \\phi\\right)} = \\left(\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right)$$"
      ],
      "text/plain": [
       "<OGRePy._core.RicciTensor at 0x78c1429ae150>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.ricci_tensor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir berechnen nun das infinitesimale Weglängenelement $ds$. Es ist wie folgt definiert\n",
    "\n",
    "$$ds^2=g_{\\mu\\nu} dx^\\mu dx^\\nu \\quad ,$$\n",
    "\n",
    "wobei $dx^\\mu = \\left(dx^0,dx^1,dx^2,dx^3 \\right) = \\left(dt,dr,d\\theta,d\\phi \\right)$ den Abstand zweier infinitesimal benachbarter Ereignisse (eine infinitesimale Raumzeitvariation) beschreibt. \n",
    "\n",
    "Das Quadrat des Linienelment $ds^2 = g_{\\mu\\nu} dx^\\mu dx^\\nu$ berechnet sich zu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\mathrm{d}\\phi^{2} r^{2} \\sin^{2}{\\left(\\theta \\right)} - \\mathrm{d}\\theta^{2} r^{2} - \\frac{\\mathrm{d}r^{2}}{- \\frac{2 M}{r} + 1} + \\mathrm{d}t^{2} \\left(- \\frac{2 M}{r} + 1\\right)$"
      ],
      "text/plain": [
       "                                                                      2        ↪\n",
       "                2  2    2                           2  2   \\mathrm{d}r         ↪\n",
       "- \\mathrm{d}\\phi ⋅r ⋅sin (\\theta) - \\mathrm{d}\\theta ⋅r  - ──────────── + \\mat ↪\n",
       "                                                              2⋅M              ↪\n",
       "                                                            - ─── + 1          ↪\n",
       "                                                               r               ↪\n",
       "\n",
       "↪                     \n",
       "↪        2 ⎛  2⋅M    ⎞\n",
       "↪ hrm{d}t ⋅⎜- ─── + 1⎟\n",
       "↪          ⎝   r     ⎠\n",
       "↪                     \n",
       "↪                     "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds2 = g.line_element()\n",
    "ds2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Geodätische Bewegung eines Probekörpers\n",
    "\n",
    "Die <i>Geodätengleichung</i> lässt sich durch folgendes Variationsprinzip herleiten\n",
    "\n",
    "\\begin{equation}\n",
    "\\int_{x^\\mu(A)}^{x^\\mu(B)} ds= \\int_{x^\\mu(A)}^{x^\\mu(B)} \\sqrt{g_{\\mu\\nu} dx^\\mu dx^\\nu}=\\int_A^B \\sqrt{g_{\\mu\\nu} \\frac{dx^\\mu}{d\\lambda} \\frac{dx^\\nu}{d\\lambda}} d\\lambda \\rightarrow \\hbox{Extremal}\n",
    "\\end{equation}\n",
    "\n",
    ", wobei man, bei festgehaltenen Anfangs- und Endpunkten ($x^\\mu(A)$ und $x^\\mu(B)$), nach den extremalsten Kurven $x^\\mu(\\lambda)$ in der Raumzeit sucht. Den Parameter $\\lambda$ bezeichnet man als affiner Parameter, welcher z.B. die Eigenzeit $\\tau$ des Körpers sein kann. Die Geod&auml;tengleichung ergibt sich dann mittels der Euler-Lagrange Gleichungen, wobei man als Lagrangedichte den Ausdruck $L = \\sqrt{g_{\\mu\\nu} \\frac{dx^\\mu}{d\\lambda} \\frac{dx^\\nu}{d\\lambda}}$, bzw. alternativ $L = g_{\\mu\\nu} \\frac{dx^\\mu}{d\\lambda} \\frac{dx^\\nu}{d\\lambda}$ verwendet.\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{d}{d\\lambda} \\left( \\frac{\\partial L}{\\partial \\frac{d x^\\alpha}{d \\lambda}} \\right) -\n",
    "    \\frac{\\partial L}{\\partial x^\\alpha} = 0 \\quad \\xrightarrow{\\cdot \\frac{1}{2}g^{\\mu \\alpha }} \\quad \\frac{d^2 x^\\mu}{d\\lambda^2} +\n",
    "    \\Gamma^\\mu_{\\nu \\rho} \\frac{d x^\\nu}{d\\lambda} \\frac{d x^\\rho}{d\\lambda} ~=~ 0\n",
    "\\end{equation}\n",
    "\n",
    "$\\Gamma^\\mu_{\\nu \\rho}$ sind die Christoffel Symbole zweiter Art und $\\lambda$ ein affiner Parameter \n",
    "(z.B. die Eigenzeit $\\tau$ des Probekörpers). Die Geodätengleichung ist ein System gekoppelter Differenzialgleichungen, das wir uns im Folgenden näher betrachten werden."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das Modul \"OGRePy\" verwendet die Lagrangedichte $L = g_{\\mu\\nu} \\frac{dx^\\mu}{d\\lambda} \\frac{dx^\\nu}{d\\lambda}$ zur Berechnung der Geod&auml;tengleichung:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$$L\\Bigg|_{\\left(t, r, \\theta, \\phi\\right)} = \\frac{\\dot{r}^{2} r^{2} - \\dot{t}^{2} \\left(2 M - r\\right)^{2} - r^{3} \\left(2 M - r\\right) \\left(\\dot{\\phi}^{2} \\sin^{2}{\\left(\\theta \\right)} + \\dot{\\theta}^{2}\\right)}{r \\left(2 M - r\\right)}$$"
      ],
      "text/plain": [
       "<OGRePy._core.Lagrangian at 0x78c1429ae2d0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.lagrangian()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Geodätengleichung mittels der Lagrangedichte $L$ berechnet lautet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$$0{}_{\\mu}\\Bigg|_{\\left(t, r, \\theta, \\phi\\right)} = \\left(\\begin{matrix}\\partial_{\\lambda} \\left(\\frac{\\dot{t} \\left(- 2 M + r\\right)}{r}\\right)\\\\\\frac{- 4 M^{3} \\dot{t}^{2} + 4 M^{2} \\dot{\\phi}^{2} r^{3} \\sin^{2}{\\left(\\theta \\right)} + 4 M^{2} \\dot{\\theta}^{2} r^{3} + 4 M^{2} \\dot{t}^{2} r + 4 M^{2} r^{2} \\partial_{\\lambda} \\left(\\frac{\\dot{r} r}{2 M - r}\\right) - 4 M \\dot{\\phi}^{2} r^{4} \\sin^{2}{\\left(\\theta \\right)} - 4 M \\dot{\\theta}^{2} r^{4} - M \\dot{r}^{2} r^{2} - M \\dot{t}^{2} r^{2} - 4 M r^{3} \\partial_{\\lambda} \\left(\\frac{\\dot{r} r}{2 M - r}\\right) + \\dot{\\phi}^{2} r^{5} \\sin^{2}{\\left(\\theta \\right)} + \\dot{\\theta}^{2} r^{5} + r^{4} \\partial_{\\lambda} \\left(\\frac{\\dot{r} r}{2 M - r}\\right)}{r^{2} \\left(4 M^{2} - 4 M r + r^{2}\\right)}\\\\\\frac{\\dot{\\phi}^{2} r^{2} \\sin{\\left(2 \\theta \\right)}}{2} + \\partial_{\\lambda} \\left(- \\dot{\\theta} r^{2}\\right)\\\\\\partial_{\\lambda} \\left(- \\dot{\\phi} r^{2} \\sin^{2}{\\left(\\theta \\right)}\\right)\\end{matrix}\\right)$$"
      ],
      "text/plain": [
       "<OGRePy._core.GeodesicFromLagrangian at 0x78c1429aea50>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.geodesic_from_lagrangian()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir benutzen im Folgenden jedoch die direkte Berechnung der Geodätengleichung mittels der Christoffel Symbole. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "$$0{}^{\\mu}\\Bigg|_{\\left(t, r, \\theta, \\phi\\right)} = \\left(\\begin{matrix}\\frac{- 2 M \\dot{r} \\dot{t} + \\ddot{t} r \\left(2 M - r\\right)}{r \\left(2 M - r\\right)}\\\\\\frac{M \\dot{r}^{2} r^{2} - M \\dot{t}^{2} \\left(2 M - r\\right)^{2} + r^{3} \\left(2 M - r\\right) \\left(\\ddot{r} + \\dot{\\phi}^{2} \\left(2 M - r\\right) \\sin^{2}{\\left(\\theta \\right)} + \\dot{\\theta}^{2} \\left(2 M - r\\right)\\right)}{r^{3} \\left(2 M - r\\right)}\\\\\\ddot{\\theta} - \\frac{\\dot{\\phi}^{2} \\sin{\\left(2 \\theta \\right)}}{2} + \\frac{2 \\dot{\\theta} \\dot{r}}{r}\\\\\\ddot{\\phi} + \\frac{2 \\dot{\\phi} \\dot{\\theta}}{\\tan{\\left(\\theta \\right)}} + \\frac{2 \\dot{\\phi} \\dot{r}}{r}\\end{matrix}\\right)$$"
      ],
      "text/plain": [
       "<OGRePy._core.GeodesicFromChristoffel at 0x78c1429aed50>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.geodesic_from_christoffel()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Geodätengleichung ist somit ein System von nichtlinearen gekoppelten Differenzialgleichungen zweiter Ordnung. Die entsprechenden vier Gleichungen lauten:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 0 = \\frac{- 2 M \\frac{d}{d \\lambda} r{\\left(\\lambda \\right)} \\frac{d}{d \\lambda} t{\\left(\\lambda \\right)} + \\left(2 M - r{\\left(\\lambda \\right)}\\right) r{\\left(\\lambda \\right)} \\frac{d^{2}}{d \\lambda^{2}} t{\\left(\\lambda \\right)}}{\\left(2 M - r{\\left(\\lambda \\right)}\\right) r{\\left(\\lambda \\right)}}$"
      ],
      "text/plain": [
       "                                                                               ↪\n",
       "             d                    d                                            ↪\n",
       "    - 2⋅M⋅────────(r(\\lambda))⋅────────(t(\\lambda)) + (2⋅M - r(\\lambda))⋅r(\\la ↪\n",
       "          d\\lambda             d\\lambda                                        ↪\n",
       "                                                                               ↪\n",
       "0 = ────────────────────────────────────────────────────────────────────────── ↪\n",
       "                                        (2⋅M - r(\\lambda))⋅r(\\lambda)          ↪\n",
       "\n",
       "↪           2                \n",
       "↪          d                 \n",
       "↪ mbda)⋅─────────(t(\\lambda))\n",
       "↪               2            \n",
       "↪       d\\lambda             \n",
       "↪ ───────────────────────────\n",
       "↪                            "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GeodEq = g.geodesic_from_christoffel().components(indices=(1,),coords=Spherical)\n",
    "GeodEq0 = Eq(0,simplify(GeodEq[0]))\n",
    "GeodEq0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "bzw. umgestellt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} t{\\left(\\lambda \\right)} = \\frac{2 M \\frac{d}{d \\lambda} r{\\left(\\lambda \\right)} \\frac{d}{d \\lambda} t{\\left(\\lambda \\right)}}{\\left(2 M - r{\\left(\\lambda \\right)}\\right) r{\\left(\\lambda \\right)}}$"
      ],
      "text/plain": [
       "                               d                    d                \n",
       "    2                   2⋅M⋅────────(r(\\lambda))⋅────────(t(\\lambda))\n",
       "   d                        d\\lambda             d\\lambda            \n",
       "─────────(t(\\lambda)) = ─────────────────────────────────────────────\n",
       "        2                       (2⋅M - r(\\lambda))⋅r(\\lambda)        \n",
       "d\\lambda                                                             "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "param = Spherical.of_param()\n",
    "dot = Spherical.of_param_dot()\n",
    "ddot = Spherical.of_param_ddot()\n",
    "\n",
    "GeodEq0_a = Eq(ddot[0],solve(GeodEq0,ddot[0])[0])\n",
    "GeodEq0_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} r{\\left(\\lambda \\right)} = \\frac{- 4 M^{2} r^{3}{\\left(\\lambda \\right)} \\sin^{2}{\\left(\\theta{\\left(\\lambda \\right)} \\right)} \\left(\\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)}\\right)^{2} - 4 M^{2} r^{3}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} \\theta{\\left(\\lambda \\right)}\\right)^{2} + M \\left(2 M - r{\\left(\\lambda \\right)}\\right)^{2} \\left(\\frac{d}{d \\lambda} t{\\left(\\lambda \\right)}\\right)^{2} + 4 M r^{4}{\\left(\\lambda \\right)} \\sin^{2}{\\left(\\theta{\\left(\\lambda \\right)} \\right)} \\left(\\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)}\\right)^{2} + 4 M r^{4}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} \\theta{\\left(\\lambda \\right)}\\right)^{2} - M r^{2}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} r{\\left(\\lambda \\right)}\\right)^{2} - r^{5}{\\left(\\lambda \\right)} \\sin^{2}{\\left(\\theta{\\left(\\lambda \\right)} \\right)} \\left(\\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)}\\right)^{2} - r^{5}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} \\theta{\\left(\\lambda \\right)}\\right)^{2}}{\\left(2 M - r{\\left(\\lambda \\right)}\\right) r^{3}{\\left(\\lambda \\right)}}$"
      ],
      "text/plain": [
       "                                                                               ↪\n",
       "                             2  3             2                  ⎛   d         ↪\n",
       "    2                   - 4⋅M ⋅r (\\lambda)⋅sin (\\theta(\\lambda))⋅⎜────────(\\ph ↪\n",
       "   d                                                             ⎝d\\lambda     ↪\n",
       "─────────(r(\\lambda)) = ────────────────────────────────────────────────────── ↪\n",
       "        2                                                                      ↪\n",
       "d\\lambda                                                                       ↪\n",
       "\n",
       "↪             2                                               2                ↪\n",
       "↪            ⎞       2  3          ⎛   d                     ⎞                 ↪\n",
       "↪ i(\\lambda))⎟  - 4⋅M ⋅r (\\lambda)⋅⎜────────(\\theta(\\lambda))⎟  + M⋅(2⋅M - r(\\ ↪\n",
       "↪            ⎠                     ⎝d\\lambda                 ⎠                 ↪\n",
       "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n",
       "↪                                                                              ↪\n",
       "↪                                                                              ↪\n",
       "\n",
       "↪                                 2                                            ↪\n",
       "↪         2 ⎛   d                ⎞         4             2                  ⎛  ↪\n",
       "↪ lambda)) ⋅⎜────────(t(\\lambda))⎟  + 4⋅M⋅r (\\lambda)⋅sin (\\theta(\\lambda))⋅⎜─ ↪\n",
       "↪           ⎝d\\lambda            ⎠                                          ⎝d ↪\n",
       "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n",
       "↪                                                                              ↪\n",
       "↪                                                                   (2⋅M - r(\\ ↪\n",
       "\n",
       "↪                        2                                              2      ↪\n",
       "↪   d                   ⎞         4          ⎛   d                     ⎞       ↪\n",
       "↪ ───────(\\phi(\\lambda))⎟  + 4⋅M⋅r (\\lambda)⋅⎜────────(\\theta(\\lambda))⎟  - M⋅ ↪\n",
       "↪ \\lambda               ⎠                    ⎝d\\lambda                 ⎠       ↪\n",
       "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n",
       "↪           3                                                                  ↪\n",
       "↪ lambda))⋅r (\\lambda)                                                         ↪\n",
       "\n",
       "↪                                   2                                          ↪\n",
       "↪  2          ⎛   d                ⎞     5             2                  ⎛    ↪\n",
       "↪ r (\\lambda)⋅⎜────────(r(\\lambda))⎟  - r (\\lambda)⋅sin (\\theta(\\lambda))⋅⎜─── ↪\n",
       "↪             ⎝d\\lambda            ⎠                                      ⎝d\\l ↪\n",
       "↪ ──────────────────────────────────────────────────────────────────────────── ↪\n",
       "↪                                                                              ↪\n",
       "↪                                                                              ↪\n",
       "\n",
       "↪                      2                                          2\n",
       "↪ d                   ⎞     5          ⎛   d                     ⎞ \n",
       "↪ ─────(\\phi(\\lambda))⎟  - r (\\lambda)⋅⎜────────(\\theta(\\lambda))⎟ \n",
       "↪ ambda               ⎠                ⎝d\\lambda                 ⎠ \n",
       "↪ ─────────────────────────────────────────────────────────────────\n",
       "↪                                                                  \n",
       "↪                                                                  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GeodEq1 = Eq(0,simplify(GeodEq[1]))\n",
    "GeodEq1_a = Eq(ddot[1],solve(GeodEq1,ddot[1])[0])\n",
    "GeodEq1_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} \\theta{\\left(\\lambda \\right)} = \\frac{\\sin{\\left(2 \\theta{\\left(\\lambda \\right)} \\right)} \\left(\\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)}\\right)^{2}}{2} - \\frac{2 \\frac{d}{d \\lambda} \\theta{\\left(\\lambda \\right)} \\frac{d}{d \\lambda} r{\\left(\\lambda \\right)}}{r{\\left(\\lambda \\right)}}$"
      ],
      "text/plain": [
       "                                                                             2 ↪\n",
       "                                                    ⎛   d                   ⎞  ↪\n",
       "    2                        sin(2⋅\\theta(\\lambda))⋅⎜────────(\\phi(\\lambda))⎟  ↪\n",
       "   d                                                ⎝d\\lambda               ⎠  ↪\n",
       "─────────(\\theta(\\lambda)) = ───────────────────────────────────────────────── ↪\n",
       "        2                                            2                         ↪\n",
       "d\\lambda                                                                       ↪\n",
       "\n",
       "↪                                                    \n",
       "↪         d                         d                \n",
       "↪    2⋅────────(\\theta(\\lambda))⋅────────(r(\\lambda))\n",
       "↪      d\\lambda                  d\\lambda            \n",
       "↪  - ────────────────────────────────────────────────\n",
       "↪                       r(\\lambda)                   \n",
       "↪                                                    "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GeodEq2 = Eq(0,simplify(GeodEq[2]))\n",
    "GeodEq2_a = Eq(ddot[2],solve(GeodEq2,ddot[2])[0])\n",
    "GeodEq2_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} \\phi{\\left(\\lambda \\right)} = - \\frac{2 \\left(\\frac{r{\\left(\\lambda \\right)} \\frac{d}{d \\lambda} \\theta{\\left(\\lambda \\right)}}{\\tan{\\left(\\theta{\\left(\\lambda \\right)} \\right)}} + \\frac{d}{d \\lambda} r{\\left(\\lambda \\right)}\\right) \\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)}}{r{\\left(\\lambda \\right)}}$"
      ],
      "text/plain": [
       "                              ⎛              d                                 ↪\n",
       "                              ⎜r(\\lambda)⋅────────(\\theta(\\lambda))            ↪\n",
       "                              ⎜           d\\lambda                       d     ↪\n",
       "    2                      -2⋅⎜──────────────────────────────────── + ──────── ↪\n",
       "   d                          ⎝        tan(\\theta(\\lambda))           d\\lambda ↪\n",
       "─────────(\\phi(\\lambda)) = ─────────────────────────────────────────────────── ↪\n",
       "        2                                                         r(\\lambda)   ↪\n",
       "d\\lambda                                                                       ↪\n",
       "\n",
       "↪             ⎞                         \n",
       "↪             ⎟                         \n",
       "↪             ⎟    d                    \n",
       "↪ (r(\\lambda))⎟⋅────────(\\phi(\\lambda)) \n",
       "↪             ⎠ d\\lambda                \n",
       "↪ ──────────────────────────────────────\n",
       "↪                                       \n",
       "↪                                       "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GeodEq3 = Eq(0,simplify(GeodEq[3]))\n",
    "GeodEq3_a = Eq(ddot[3],solve(GeodEq3,ddot[3])[0])\n",
    "GeodEq3_a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Radiales Einfallen eines Probekörpers in ein schwarzes Loch\n",
    "\n",
    "Wir lassen im Folgenden nur ebene Bewegungen zu ($\\theta=\\frac{\\pi}{2}, {\\rm cos}(\\theta)=0, {\\rm sin}(\\theta)=1, \\frac{d \\theta}{d\\tau}=0, \\frac{d^2 \\theta}{d\\tau^2}=0$) und beschränken uns zusätzlich auf ein radial in das schwarze Loch einfallenden Probekörper ($\\frac{d \\phi}{d\\tau}=0, \\frac{d^2 \\phi}{d\\tau^2}=0$). Unter diesen Annahmen sind nur die ersten beiden Geodätengleichungen relevant und diese lauten dann:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} t{\\left(\\lambda \\right)} = \\frac{2 M \\frac{d}{d \\lambda} r{\\left(\\lambda \\right)} \\frac{d}{d \\lambda} t{\\left(\\lambda \\right)}}{\\left(2 M - r{\\left(\\lambda \\right)}\\right) r{\\left(\\lambda \\right)}}$"
      ],
      "text/plain": [
       "                               d                    d                \n",
       "    2                   2⋅M⋅────────(r(\\lambda))⋅────────(t(\\lambda))\n",
       "   d                        d\\lambda             d\\lambda            \n",
       "─────────(t(\\lambda)) = ─────────────────────────────────────────────\n",
       "        2                       (2⋅M - r(\\lambda))⋅r(\\lambda)        \n",
       "d\\lambda                                                             "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GeodEq0_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} r{\\left(\\lambda \\right)} = \\frac{M \\left(2 M - r{\\left(\\lambda \\right)}\\right)^{2} \\left(\\frac{d}{d \\lambda} t{\\left(\\lambda \\right)}\\right)^{2} - M r^{2}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} r{\\left(\\lambda \\right)}\\right)^{2}}{\\left(2 M - r{\\left(\\lambda \\right)}\\right) r^{3}{\\left(\\lambda \\right)}}$"
      ],
      "text/plain": [
       "                                                                    2          ↪\n",
       "                                            2 ⎛   d                ⎞       2   ↪\n",
       "    2                   M⋅(2⋅M - r(\\lambda)) ⋅⎜────────(t(\\lambda))⎟  - M⋅r (\\ ↪\n",
       "   d                                          ⎝d\\lambda            ⎠           ↪\n",
       "─────────(r(\\lambda)) = ────────────────────────────────────────────────────── ↪\n",
       "        2                                                              3       ↪\n",
       "d\\lambda                                           (2⋅M - r(\\lambda))⋅r (\\lamb ↪\n",
       "\n",
       "↪                               2\n",
       "↪         ⎛   d                ⎞ \n",
       "↪ lambda)⋅⎜────────(r(\\lambda))⎟ \n",
       "↪         ⎝d\\lambda            ⎠ \n",
       "↪ ───────────────────────────────\n",
       "↪                                \n",
       "↪ da)                            "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GeodEq1_a = GeodEq1_a.subs({(param[2],pi/2),(dot[2],0),(dot[3],0)})\n",
    "GeodEq1_a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es ist manchmal hilfreich auch eine Latex-Ausgabe der DGL zu erzeugen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\frac{d^{2}}{d \\lambda^{2}} t{\\left(\\lambda \\right)} = \\frac{2 M \\frac{d}{d \\lambda} r{\\left(\\lambda \\right)} \\frac{d}{d \\lambda} t{\\left(\\lambda \\right)}}{\\left(2 M - r{\\left(\\lambda \\right)}\\right) r{\\left(\\lambda \\right)}}\n",
      "\\frac{d^{2}}{d \\lambda^{2}} r{\\left(\\lambda \\right)} = \\frac{M \\left(2 M - r{\\left(\\lambda \\right)}\\right)^{2} \\left(\\frac{d}{d \\lambda} t{\\left(\\lambda \\right)}\\right)^{2} - M r^{2}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} r{\\left(\\lambda \\right)}\\right)^{2}}{\\left(2 M - r{\\left(\\lambda \\right)}\\right) r^{3}{\\left(\\lambda \\right)}}\n"
     ]
    }
   ],
   "source": [
    "print(latex(GeodEq0_a))\n",
    "print(latex(GeodEq1_a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Um dieses System von zwei Differenzialgleichungen zweiter Ordnung mit Python numerisch lösen zu können, müssen wir es zunächst in ein System von vier Differenzialgleichungen erster Ordnung umschreiben. Details zum numerischen Lösung von Differenzialgleichungen finden Sie in der Vorlesung <A href=\"https://itp.uni-frankfurt.de/~hanauske/VPROG/index.html\" target=\"_blank\">Einführung in die Programmierung für Studierende der Physik</A> in den Unterpunkten <A href=\"https://itp.uni-frankfurt.de/~hanauske/VPROG/V8/DGL_1.html\" target=\"_blank\">Differenzialgleichungen: Numerische Lösung von Anfangswertproblemen</A> und \n",
    "<A href=\"https://itp.uni-frankfurt.de/~hanauske/VPROG/V9/DGL_2.html\" target=\"_blank\">Systeme von gekoppelten Differenzialgleichungen und Differenzialgleichungen zweiter Ordnung</A>.\n",
    "\n",
    "Wir definieren dazu formal\n",
    "$$\n",
    "t(\\tau) = y_1(\\tau) \\, , \\quad r(\\tau) = y_2(\\tau) \\, , \\quad \\frac{d t(\\tau)}{d\\tau} = y_3(\\tau) \\, , \\quad \\frac{d r(\\tau)}{d\\tau} = y_4(\\tau)\n",
    "$$\n",
    "\n",
    "und schreiben unser DGL-System wie folgt um:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\frac{d^2 t(\\tau)}{d\\tau^2} &=& \\frac{d y_3(\\tau)}{d\\tau} = f_3(\\tau,y_1,y_2,y_3,y_4) = \\frac{2 M \\frac{d}{d \\tau} r{\\left(\\tau \\right)} \\frac{d}{d \\tau} t{\\left(\\tau \\right)}}{r \\left(2 M - r\\right)} \\\\\n",
    "\\frac{d^2 r(\\tau)}{d\\tau^2} &=& \\frac{d y_4(\\tau)}{d\\tau} = f_4(\\tau,y_1,y_2,y_3,y_4) =  \\\\\n",
    "&=&\n",
    "\\frac{M \\left(- 4 M^{2} \\left(\\frac{d}{d \\tau} t{\\left(\\tau \\right)}\\right)^{2} + 4 M r \\left(\\frac{d}{d \\tau} t{\\left(\\tau \\right)}\\right)^{2} + r^{2} \\left(\\frac{d}{d \\tau} r{\\left(\\tau \\right)}\\right)^{2} - r^{2} \\left(\\frac{d}{d \\tau} t{\\left(\\tau \\right)}\\right)^{2}\\right)}{r^{3} \\left(- 2 M + r\\right)}\n",
    "\\end{eqnarray}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "y1, y2, y3, y4 = symbols('y_1, y_2, y_3, y_4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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otltgcHjqMWBRQVsMRccaH3v9hjJG9sg2wFkotcKhSYDzzXU0qCuVS79PT8hGmEJuiQuIGz0PgmgI8wj78MCnCKvL2MsSmVoI7eTadrTDXV54Rd5fvVDO+yjOP8nlE0MXbtcPAjifc9aa+56M7o8dtpAx0UUvQmhntGNfKiuMX8bKjuY+9l2B3cmykBxxinym1jsb/x/moDvcpyQ9qAAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} t{\\left(\\lambda \\right)} = \\frac{2 M y_{3} y_{4}}{y_{2} \\left(2 M - y_{2}\\right)}$"
      ],
      "text/plain": [
       "    2                                \n",
       "   d                      2⋅M⋅y₃⋅y₄  \n",
       "─────────(t(\\lambda)) = ─────────────\n",
       "        2               y₂⋅(2⋅M - y₂)\n",
       "d\\lambda                             "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SysDGL_0 = Eq(ddot[0],GeodEq0_a.rhs.subs({(param[1],y2),(dot[0],y3),(dot[1],y4)}))\n",
    "SysDGL_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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30NlHU1laZWKFu6B6vXlnZTuNwbQZPiODN6qYVZ+VvnR0DaBvJEBs+4pBNFgC0GFlLBnYJuYm0dRnwGNJ63vq8xv9CRGQ/KEU3Y7Iy2Lpac9Ek1ugMVT4zZabpDIKlHkwZCBQDxpeOgfFq3QnqD5GDuf3jb5TvvcbjynYpvjtvWuLtr9GMRcFRAAjbAh8UaGJDoFlpQw/T6j0IkG83fMV11hC2Wf6umyzqo7JZZm0zE0hoLFEUfKzsPHLO2SFUFKOGA9DcuCUq3gaH8cs+nMTpeMkcg9P3HpZ5a1y8qG51QWfjvtQ9w8l0MdnD6Uzp+jHdczUCwbKE+D4CUGEEKF+pasUsCzw4TERegLr+fJyBOv74O+Jec4iwfNiuzorqP7surMe2CrNRkBjhdLCssQlgG83WLa+7E4xftl7XbyYi+UMQwMZxSodCsgpst8L8O1lvs9wyl/l2ReAUR1eVtP+XHA/uSke5hrMtiFX8RR5akcVzjOeTb/AOIzbDB4PukqwmDUICCwvR+xoG4rKfEFjAmJuBBOoAJr4YgVQzguTmn/HEuq2RENgAAFeyiGfWJQmo0aKJYbFawFFCj2GAzsqFMLYrg1rGgVaFZBrESLndlKjU0/llNkRUbdI+LxAp3vabIrKDJgxJR/qnygxBecpTQBbMGlhAAFnMUsoWBndD/woHVsXpDmZgYVRClglBNwZqeWJQMLfBFNJZzUXXR+OqP1pCCQISBZRgm99NgrMZM8oyQuGhOhRblMVHPKa8jX+uZi5ww+jp7JvtBg91iabX/TDlDTPO6i+zbOYnqKzB7WlGmfR0v6XvpGmcAc/IhMd2Bqdr9aiGAGnmJWB1YEbwlZso0FA7IiP5XViPyhOqaug96ttKh/9t08dhu2mIVBGgBfRpmixjlM3GzKb5pU59ktvlWVKsl8a5agt7AZp05CLA2osdDe3aLsu8mLF9EJ5TqkrJh9FN8m/rHrU+cXXVVQVcPcYlmmFKTgz74OhpTSYYIgNnT5hQaK9LQwgYIoZAbcV3ZH6gUZIBgVENJSjlDmGREDBM0BhkMhsoSGwFAKSOacwFaOAmdzBmFAeVh55HVnW/UmCnofrjv/Y7VwPEx5CH5zSUl1cGLHxQ78Ik/ogPvBc7LST53dQXIMzC0v8/x7RA+Thuswp/uqFDyAuMVwLOASZK1XAKOuDyrMConwmAUrZvWTxtAgY9ZpiBpAWTokAFmrqZkOJ8MLPKQPFyPWULba19y8lqDsYxBuFyn/rDpay0s4KVmzuioPSzJOOG0/3lHNe3j0jplc+Sj70Qem1wyjOaiDzndMmtYF+g3ELAwhcR/lBmHweAmICjhAyCRyNFza2TelWiC1M6VfbVNxCQ2ARBFCCOZmNDYmpW2xrmFOcdpPGXv6fKE5f9sUv8Kwai0VsEZMPf/KxKlO/NPlxH3S7ahjFWX0IuxbfUhR17ApJO4DFnI5dSnPR91cC9V4IIAhutQcN5SFgrPS2CvK1lANSMYKDBYBzvyNA/h66ZjELhBZOikBnYnu5RDbjnR+KjzwLbLGxVJHtUsAgeZIjUF3mCTtF3slw0ihcyuMcPPMpDrmz8W9FgNXYUdiqS7vIj/ug21VDDc6hgb4P6I+SW8U+Yw/1WqKLwLW/ZbvC2c+vFX+o67UuLGYsDvKwhC1gJSBsHaGyQsWU429iAnQGNaJpyYbAsQggZ8gsyvadLnvRFBsLU7fY1ibkH+WbCyhNlHPvaKjy3A6TSmoX9VG0zAMMGRS4WZbQcSzVzQ/FLB601RYMO/NfOtkg8rOEGpxdQ9QPcGE8xo4jWn/P0oE9PqT463J77FBr82UiIKWAQniqeNBS8zS42kyJD4IlGs7apq66QfpLKfAY9nBWPkqZBcXtlv39QXHHOPP57dcbRwTGLOYRslbcENgOAprcHSWse7b/WLDPh1opGqzRsS12XJ1noGScookLLiVdi7PoUMrsqlHMZvWDG9Z2GsgD2xYKCFwVylpRQ2CrCKBgX0eNu1OaXzHMute84kAZjG2xA0vVwe2AGwKlc6mhFmdcNbgniO3Cv9/xt3sswdRcOpeK62i/m8U8ClEj2CACWF2cH+b9B24J/Lexbzk02SsD89ke/D1xZ4sdKnQTvHvBV8z7lksMVTgLy9qPyLCqL3YHMkWAmo95ClqNdlcIeCXstthRw90WW2Uday4q7yQ9D/fjQp2CdjMJAeHIIspn6zUL4iTeD5G4KeaHOKqtTw4BKYG/lcD/3AnKf9TJaDcNgY0h8H9Yd72HruYfOAAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} r{\\left(\\lambda \\right)} = \\frac{- M y_{2}^{2} y_{4}^{2} + M y_{3}^{2} \\left(2 M - y_{2}\\right)^{2}}{y_{2}^{3} \\left(2 M - y_{2}\\right)}$"
      ],
      "text/plain": [
       "    2                         2   2       2           2\n",
       "   d                    - M⋅y₂ ⋅y₄  + M⋅y₃ ⋅(2⋅M - y₂) \n",
       "─────────(r(\\lambda)) = ───────────────────────────────\n",
       "        2                         3                    \n",
       "d\\lambda                        y₂ ⋅(2⋅M - y₂)         "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SysDGL_1 = Eq(ddot[1],GeodEq1_a.rhs.subs({(param[1],y2),(dot[0],y3),(dot[1],y4)}))\n",
    "SysDGL_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diese beiden DGLs werden wir später zusätzlich mittels der Programmiersprache C++ lösen. Wir exportieren deshalb schon jetzt das zugrundeliegende System von DGLs als C++ Code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.codegen.ast import Assignment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "wert = 2*M*y_3*y_4/(y_2*(2*M - y_2));\n",
      "wert = (-M*pow(y_2, 2)*pow(y_4, 2) + M*pow(y_3, 2)*pow(2*M - y_2, 2))/(pow(y_2, 3)*(2*M - y_2));\n"
     ]
    }
   ],
   "source": [
    "wert = symbols('wert')\n",
    "print(ccode(Assignment(wert,SysDGL_0.rhs)))\n",
    "print(ccode(Assignment(wert,SysDGL_1.rhs)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es ist manchmal hilfreich auch eine Latex-Ausgabe der DGL zu erzeugen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\frac{d^{2}}{d \\lambda^{2}} t{\\left(\\lambda \\right)} = \\frac{2 M y_{3} y_{4}}{y_{2} \\left(2 M - y_{2}\\right)}\n",
      "\\frac{d^{2}}{d \\lambda^{2}} r{\\left(\\lambda \\right)} = \\frac{- M y_{2}^{2} y_{4}^{2} + M y_{3}^{2} \\left(2 M - y_{2}\\right)^{2}}{y_{2}^{3} \\left(2 M - y_{2}\\right)}\n"
     ]
    }
   ],
   "source": [
    "print(latex(SysDGL_0))\n",
    "print(latex(SysDGL_1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun lösen wir die DGLs mittels Python und setzen im Folgenden $M=1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_3 = lambdify((y1,y2,y3,y4), SysDGL_0.rhs.subs(M,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_4 = lambdify((y1,y2,y3,y4), SysDGL_1.rhs.subs(M,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir berechnen nun die numerische Lösung des oben beschriebenen Systems bestehend aus zwei gekoppelten DGLs.\n",
    "\n",
    "Wir benutzen hierfür das Python-Modul <A href=\"https://docs.scipy.org/doc/scipy/tutorial/index.html#user-guide\" target=\"_blank\">SciPy</A>, welches eine breite Kollektion von mathematischen Algorithmen und Funktionen bereitstellt. Im Speziellen werden wir in diesem Semester die Funktion <A href=\"https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp\" target=\"_blank\">'solve_ivp(...)'</A> verwenden, die sich im Untermodul <A href=\"https://docs.scipy.org/doc/scipy/reference/integrate.html#module-scipy.integrate\" target=\"_blank\">'scipy.integrate'</A> befindet, welches Funktionen zum Lösen von gewöhnlichen Differenzialgleichungen bereitstellt. Zusätzlich berechnen wir die numerische Lösung auch mittels der älteren Methode \"integrate.odeint()\", die ebenfalls in dem Python-Modul \"scipy\" definiert ist. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "from matplotlib import rcParams\n",
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir definieren das System der gekoppelten vier Differenzialgleichungen erster Ordnung:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def DGLsys(time, vy):\n",
    "    y1,y2,y3,y4 = vy\n",
    "    dy1 = y3\n",
    "    dy2 = y4\n",
    "    dy3 = f_3(y1,y2,y3,y4)\n",
    "    dy4 = f_4(y1,y2,y3,y4)\n",
    "    return np.array([dy1,dy2,dy3,dy4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zusätzlich auch für die ältere Methode \"integrate.odeint()\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def DGLsys_odeint(vy, time):\n",
    "    y1,y2,y3,y4 = vy\n",
    "    dy1 = y3\n",
    "    dy2 = y4\n",
    "    dy3 = f_3(y1,y2,y3,y4)\n",
    "    dy4 = f_4(y1,y2,y3,y4)\n",
    "    return np.array([dy1,dy2,dy3,dy4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zum Vergleich lösen wir auch die Bewegungsgleichung nach Newton: \n",
    "\n",
    "$$\\frac{d^2r}{dt^2}=-\\frac{1}{r^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def DGLsysNewton(time, vy):\n",
    "    r, y2 = vy\n",
    "    dr = y2\n",
    "    dy2 = -1/r**2\n",
    "    return np.array([dr,dy2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zusätzlich auch für die ältere Methode \"integrate.odeint()\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def DGLsysNewton_odeint(vy, time):\n",
    "    r, y2 = vy\n",
    "    dr = y2\n",
    "    dy2 = -1/r**2\n",
    "    return np.array([dr,dy2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Abhängigkeit von den Anfangswerten können unterschiedliche Bahnen der Bewegung entstehen. Wir wählen zunächst als Beispiel die Anfangswerte eines Probekörpers, der sich zur Zeit $t=\\tau=0$ bei einem Radius von $r_0=10=5 R_S$ befindet und eine Anfangsgeschwindigkeit in radialer Richtung von $\\left. \\frac{dr}{d\\tau} \\right|_{\\tau=0}=0$ hat. Die weitere nötige Anfangsbedingung ( $\\left. \\frac{dt}{d\\tau} \\right|_{\\tau=0}$ ) erhalten wir mittels der Bedingung $\\left( \\frac{ds}{d\\tau} \\right)^2= g_{\\mu\\nu} \\frac{dx^\\mu}{d\\tau} \\frac{dx^\\nu}{d\\tau} = g_{\\mu\\nu} u^\\mu u^\\nu = 1$, die für massive Probekörper immer erfüllt sein muss ($u^\\mu$ ist die Vierergeschwindigkeit des Probekörpers). Wir beschreiben die Bewegung aus der Sichtweise eines im Unendlichen ruhenden Beobachters (Schwarzschild Koordinaten). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10000\n",
    "tval = np.linspace(0, 33.7, N+1)\n",
    "tvalNewton = np.linspace(0, 35.12, N+1)\n",
    "\n",
    "t0 = 0.0\n",
    "r0 = 10.0\n",
    "dr0 = 0.0\n",
    "dt0 = 1/np.sqrt(1-2/r0)\n",
    "\n",
    "initialval = np.array([t0,r0,dt0,dr0])\n",
    "initialvalNewton = np.array([r0,dr0])\n",
    "\n",
    "Loes = integrate.solve_ivp(DGLsys, [tval[0], tval[-1]], initialval, t_eval=tval)\n",
    "LoesNewton = integrate.solve_ivp(DGLsysNewton, [tvalNewton[0], tvalNewton[-1]], initialvalNewton, t_eval=tvalNewton)\n",
    "\n",
    "Loes_odeint = integrate.odeint(DGLsys_odeint, initialval, tval)\n",
    "LoesNewton_odeint = integrate.odeint(DGLsysNewton_odeint, initialvalNewton, tvalNewton)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "rcParams.update({\n",
    "    'figure.figsize'    : [10,8],\n",
    "    'axes.titlesize' : 14,\n",
    "    'axes.labelsize' : 16,  \n",
    "    'xtick.labelsize' : 14 ,\n",
    "    'ytick.labelsize' : 14 \n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.cla()\n",
    "plt.ylabel(r\"$\\rm Koordinaten \\, Zeit \\,\\,t$\")\n",
    "plt.xlabel(r\"$\\rm Radius \\,\\,r$\")\n",
    "plt.xlim(0,10.1)\n",
    "plt.ylim(0,57)\n",
    "\n",
    "plt.plot(Loes.y[1],Loes.y[0],c=\"blue\", linewidth=1.5, linestyle='-',label=\"Allgemeine Relativitätstheorie\");\n",
    "plt.plot(LoesNewton.y[0],tval,c=\"red\", linewidth=1.5, linestyle='-',label=\"Newton\");\n",
    "plt.legend(loc='upper right', fontsize=18)\n",
    "\n",
    "plt.axvline(x=2, linewidth=1.5, color=\"black\", linestyle=':')\n",
    "plt.text(2, 5, r\"$R_S=2M$\", size=20, rotation=0.,ha=\"center\", va=\"center\",\n",
    "         bbox=dict(boxstyle=\"round\",ec=\"black\",fc=\"white\"));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zusätzlich auch für die ältere Methode \"integrate.odeint()\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.cla()\n",
    "plt.ylabel(r\"$\\rm Koordinaten \\, Zeit \\,\\,t$\")\n",
    "plt.xlabel(r\"$\\rm Radius \\,\\,r$\")\n",
    "plt.xlim(0,10.1)\n",
    "plt.ylim(0,57)\n",
    "\n",
    "\n",
    "plt.plot(Loes_odeint[:, 1],Loes_odeint[:, 0],c=\"blue\", linewidth=1.5, linestyle='-',label=\"Allgemeine Relativitätstheorie\");\n",
    "plt.plot(LoesNewton_odeint[:, 0],tval,c=\"red\", linewidth=1.5, linestyle='-',label=\"Newton\");\n",
    "plt.legend(loc='upper right', fontsize=18)\n",
    "\n",
    "plt.axvline(x=2, linewidth=1.5, color=\"black\", linestyle=':')\n",
    "plt.text(2, 5, r\"$R_S=2M$\", size=20, rotation=0.,ha=\"center\", va=\"center\",\n",
    "         bbox=dict(boxstyle=\"round\",ec=\"black\",fc=\"white\"));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der in das schwarze Loch fallende Probekörpers bleibt somit, für einen äußeren Beobachter, anscheinend am Ereignishorizont bei $R_S=2M$ stehen (siehe die blaue Kurve im oberen Raumzeitdiagramm). Seine Bewegung in radialer Richtung wird nahe dem Ereignishorizont immer langsamer und das Bild, welches ein äußerer Beobachter wahrnimmt, friert am Ereignishorizont ein. Man kann zeigen, dass das wahrgenommene Bild gleichzeitig unendlich rotverschoben wird, sodass es nahe dem Ereignishorizont, langsam den wahrnehmbaren, sichtbaren Bereich verlässt.\n",
    "\n",
    "Eine gute und zugleich lehrreiche Verbildlichung dieser und weiterer seltsamen Eigenschaften von schwarzen Löchern findet sich in dem Essay <i>Black Holes and the German Reichstag</i> (Schwarze Löcher und der Deutsche Reichstag) welcher 2005 im Magazin Physics World erschien (siehe <A href=\"https://itp.uni-frankfurt.de/~hanauske/VARTC/2026/LateralThougts.html\" target=\"_blank\">Black Holes and the German Reichstag</A>)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die untere Abbildung veranschaulicht zusätzlich zur Lösung des radialen Falls des Probekörpers einige radial nach Außen gesendete Lichtstrahlen (gepunktete rote Kurven)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.cla()\n",
    "plt.ylabel(r\"$\\rm Koordinaten \\, Zeit \\,\\,t$\")\n",
    "plt.xlabel(r\"$\\rm Radius \\,\\,r$\")\n",
    "plt.xlim(0,10.1)\n",
    "plt.ylim(0,80)\n",
    "\n",
    "plt.plot(Loes.y[1],Loes.y[0],c=\"blue\", linewidth=1.5, linestyle='-',label=\"Allgemeine Relativitätstheorie\");\n",
    "\n",
    "positions = [8, 6, 4, 3, 2.3, 2.1, 2.05, 2.01]\n",
    "for pos in positions:\n",
    "    rval = np.linspace(pos, 10, 1000)\n",
    "    it = np.where(Loes.y[1] < pos)\n",
    "    PhotonOut = 2*np.log(np.abs(rval-2))+rval-(2*np.log(np.abs(pos-2))+pos)+Loes.y[0][it[0][0]]\n",
    "    plt.plot(rval, PhotonOut, c=\"red\", linewidth=1.5, linestyle=\":\")\n",
    "\n",
    "plt.legend(loc='lower center', fontsize=18)\n",
    "\n",
    "plt.axvline(x=2, linewidth=1.5, color=\"black\", linestyle=':')\n",
    "plt.text(2, 15, r\"$R_S=2M$\", size=20, rotation=0.,ha=\"center\", va=\"center\",\n",
    "         bbox=dict(boxstyle=\"round\",ec=\"black\",fc=\"white\"));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zusätzlich auch für die ältere Methode \"integrate.odeint()\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.cla()\n",
    "plt.ylabel(r\"$\\rm Koordinaten \\, Zeit \\,\\,t$\")\n",
    "plt.xlabel(r\"$\\rm Radius \\,\\,r$\")\n",
    "plt.xlim(0,10.1)\n",
    "plt.ylim(0,80)\n",
    "\n",
    "plt.plot(Loes_odeint[:, 1],Loes_odeint[:, 0],c=\"blue\", linewidth=1.5, linestyle='-',label=\"Allgemeine Relativitätstheorie\");\n",
    "\n",
    "positions = [8, 6, 4, 3, 2.3, 2.1, 2.05, 2.01]\n",
    "for pos in positions:\n",
    "    rval = np.linspace(pos, 10, 1000)\n",
    "    it = np.where(Loes_odeint[:, 1] < pos)\n",
    "    PhotonOut = 2*np.log(np.abs(rval-2))+rval-(2*np.log(np.abs(pos-2))+pos)+Loes_odeint[it[0][0],0]\n",
    "    plt.plot(rval, PhotonOut, c=\"red\", linewidth=1.5, linestyle=\":\")\n",
    "\n",
    "plt.legend(loc='lower center', fontsize=18)\n",
    "\n",
    "plt.axvline(x=2, linewidth=1.5, color=\"black\", linestyle=':')\n",
    "plt.text(2, 15, r\"$R_S=2M$\", size=20, rotation=0.,ha=\"center\", va=\"center\",\n",
    "         bbox=dict(boxstyle=\"round\",ec=\"black\",fc=\"white\"));"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "ART_env",
   "language": "python",
   "name": "art_env"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.14.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}