{
"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 II: Klassifizierung unterschiedlicher Bahnbewegungen"
]
},
{
"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 extremalsten Kurve, in der durch die Metrik beschriebenen gekrümmten Raumzeit, vollzieht. \n",
"\n",
"Die Geodätengleichung 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 Geodätengleichung 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": [
"Wir betrachten im Folgenden die Geodätengleichung in vorgegebener Schwarzschild-Raumzeit\n",
"\n",
"$$ g_{\\mu\\nu}=\\left( \\begin{array}{ccc} 1-\\frac{2\\,M}{r} & 0 & 0 & 0\\\\ 0& -\\frac{1}{1-\\frac{2\\,M}{r}}& 0&0 \\\\ 0& 0& -r^2& 0\\\\ 0& 0& 0& -r^2 \\hbox{sin}^2(\\theta)\\\\ \\end{array} \\right) \n",
"$$\n",
"\n",
", wobei wir wieder ein sphärisches Koordinatensystem benutzen ($x^\\mu=\\left(t,r,\\theta,\\phi \\right)$). Die Geodätengleichung stellt ein System gekoppelter nichtlinearer Differenzialgleichungen dar\n",
"\n",
"$$\n",
"\\begin{eqnarray}\n",
"&& \\frac{d^2 t}{d\\lambda^2} = - \\Gamma^0_{\\nu \\rho} \\frac{d x^\\nu}{d\\lambda} \\frac{d x^\\rho}{d\\lambda} \\\\\n",
"&& \\frac{d^2 r}{d\\lambda^2} = - \\Gamma^1_{\\nu \\rho} \\frac{d x^\\nu}{d\\lambda} \\frac{d x^\\rho}{d\\lambda}\\\\\n",
"&& \\frac{d^2 \\theta}{d\\lambda^2} = - \\Gamma^2_{\\nu \\rho} \\frac{d x^\\nu}{d\\lambda} \\frac{d x^\\rho}{d\\lambda}\\\\\n",
"&& \\frac{d^2 \\phi}{d\\lambda^2} = - \\Gamma^3_{\\nu \\rho} \\frac{d x^\\nu}{d\\lambda} \\frac{d x^\\rho}{d\\lambda} \\quad ,\n",
"\\end{eqnarray}\n",
"$$\n",
"\n",
"wobei $\\lambda$ ein affiner Parameter (z.B. die Eigenzeit $\\tau$), t, r, $\\theta$ und $\\phi$ die Koordinaten und $\\Gamma^\\mu_{\\nu \\rho}$ die Christoffel Symbole zweiter Art darstellen."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"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: OGRePy-Documentation. Dann definieren wir die zugrundeliegenden Koordinaten und die kovariante Form der Raumzeit-Metrik der Schwarzschildmetrik."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/markdown": [
"\n",
"OGRePy: An Object-Oriented General Relativity Package for Python
\n",
"By Barak Shoshany (baraksh@gmail.com) (baraksh.com)
\n",
"v2.0.0 (2026-05-11)
\n",
"GitHub repository: https://github.com/bshoshany/OGRePy
\n",
"Documentation: .ipynb, .pdf, .html\n",
""
],
"text/plain": [
""
]
},
"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": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"g.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Geodätische Bewegung eines Probekörpers\n",
"\n",
"Um die Geodätengleichung \n",
"\n",
"$$\n",
"\\frac{d^2 x^\\mu}{d\\lambda^2} + \\Gamma^\\mu_{\\nu \\rho} \\frac{d x^\\nu}{d\\lambda} \\frac{d x^\\rho}{d\\lambda} ~=~ 0 \n",
"$$\n",
"\n",
"zu berechnen, verwenden wir im Folgenden die direkte Berechnung der Geodätengleichung mittels der Christoffel Symbole. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/markdown": [
"**OGRePy**: You have the latest version of the package."
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"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": [
""
]
},
"execution_count": 4,
"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": 5,
"metadata": {},
"outputs": [
{
"data": {
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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": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"param = Spherical.of_param()\n",
"dot = Spherical.of_param_dot()\n",
"ddot = Spherical.of_param_ddot()\n",
"\n",
"GeodEq = g.geodesic_from_christoffel().components(indices=(1,),coords=Spherical)\n",
"GeodEq0 = Eq(0,simplify(GeodEq[0]))\n",
"GeodEq0_a = Eq(ddot[0],solve(GeodEq0,ddot[0])[0])\n",
"GeodEq0_a"
]
},
{
"cell_type": "code",
"execution_count": 6,
"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": 6,
"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": 7,
"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": 7,
"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": 8,
"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": 8,
"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": [
"### Beispiel einer gebundenen elliptischen Bahn\n",
"\n",
"Wir lassen im Folgenden nur ebene Bewegungen zu ($\\theta=\\frac{\\pi}{2}, {\\rm cos}(\\theta)=0, {\\rm sin}(\\theta)=1, \\frac{d \\theta}{d\\tau}=0, \\frac{d^2 \\theta}{d\\tau^2}=0$). Unter diesen Annahmen sind nur drei der vier Geodätengleichungen relevant und diese lauten dann:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"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": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"GeodEq0_a"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/latex": [
"$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} r{\\left(\\lambda \\right)} = \\frac{- 4 M^{2} r^{3}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)}\\right)^{2} + M \\left(2 M - r{\\left(\\lambda \\right)}\\right)^{2} \\left(\\frac{d}{d \\lambda} t{\\left(\\lambda \\right)}\\right)^{2} + 4 M r^{4}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)}\\right)^{2} - M r^{2}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} r{\\left(\\lambda \\right)}\\right)^{2} - r^{5}{\\left(\\lambda \\right)} \\left(\\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)}\\right)^{2}}{\\left(2 M - r{\\left(\\lambda \\right)}\\right) r^{3}{\\left(\\lambda \\right)}}$"
],
"text/plain": [
" 2 ↪\n",
" 2 3 ⎛ d ⎞ ↪\n",
" 2 - 4⋅M ⋅r (\\lambda)⋅⎜────────(\\phi(\\lambda))⎟ + M⋅(2⋅M ↪\n",
" d ⎝d\\lambda ⎠ ↪\n",
"─────────(r(\\lambda)) = ────────────────────────────────────────────────────── ↪\n",
" 2 ↪\n",
"d\\lambda ↪\n",
"\n",
"↪ 2 ↪\n",
"↪ 2 ⎛ d ⎞ 4 ⎛ d ↪\n",
"↪ - r(\\lambda)) ⋅⎜────────(t(\\lambda))⎟ + 4⋅M⋅r (\\lambda)⋅⎜────────(\\phi(\\la ↪\n",
"↪ ⎝d\\lambda ⎠ ⎝d\\lambda ↪\n",
"↪ ──────────────────────────────────────────────────────────────────────────── ↪\n",
"↪ 3 ↪\n",
"↪ (2⋅M - r(\\lambda))⋅r (\\lambda) ↪\n",
"\n",
"↪ 2 2 ↪\n",
"↪ ⎞ 2 ⎛ d ⎞ 5 ⎛ d ↪\n",
"↪ mbda))⎟ - M⋅r (\\lambda)⋅⎜────────(r(\\lambda))⎟ - r (\\lambda)⋅⎜────────(\\ph ↪\n",
"↪ ⎠ ⎝d\\lambda ⎠ ⎝d\\lambda ↪\n",
"↪ ──────────────────────────────────────────────────────────────────────────── ↪\n",
"↪ ↪\n",
"↪ ↪\n",
"\n",
"↪ 2\n",
"↪ ⎞ \n",
"↪ i(\\lambda))⎟ \n",
"↪ ⎠ \n",
"↪ ─────────────\n",
"↪ \n",
"↪ "
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"GeodEq1_a = GeodEq1_a.subs({(param[2],pi/2),(dot[2],0)})\n",
"GeodEq1_a"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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caP2m7AKFA9M4IBlDTgltTzaEmIkqeJt1ohwf8ibrmeUgbhef/vKtAJuJKDSewSV5it2Ri5LmWBCPILaxyLHPU71nwAoUDszNAeTK/Q5mH+5bFWBSCwFyOlaOmRBzjFGo3c3mJW8tbpbqQljhQCYHNClxFDnbbVY7yR3yJqvzDDJZW4oVDuyOA3i6cy5b8SjAeTgoxuBwQ1o65HNAMznfzvBx0uRlq8UBrvb3OH6Tu00XY7DboSuED+DAXLdZzefPA9rdVdGyZ7Cr4SrEjuWAndVH/2yZ6rOR/kbx4Y4UHU//BdWk0kFo5YSBAAAAAElFTkSuQmCC",
"text/latex": [
"$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} \\phi{\\left(\\lambda \\right)} = - \\frac{2 \\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)} \\frac{d}{d \\lambda} r{\\left(\\lambda \\right)}}{r{\\left(\\lambda \\right)}}$"
],
"text/plain": [
" d d \n",
" 2 -2⋅────────(\\phi(\\lambda))⋅────────(r(\\lambda)) \n",
" d d\\lambda d\\lambda \n",
"─────────(\\phi(\\lambda)) = ────────────────────────────────────────────────\n",
" 2 r(\\lambda) \n",
"d\\lambda "
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"GeodEq3_a = GeodEq3_a.subs({(param[2],pi/2),(dot[2],0)})\n",
"GeodEq3_a"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Die zweite, radiale Differenzialgleichung lässt sich noch weiter umformen."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/latex": [
"$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} r{\\left(\\lambda \\right)} = \\frac{M \\left(2 M - r{\\left(\\lambda \\right)}\\right) \\left(\\frac{d}{d \\lambda} t{\\left(\\lambda \\right)}\\right)^{2}}{r^{3}{\\left(\\lambda \\right)}} - \\frac{M \\left(\\frac{d}{d \\lambda} r{\\left(\\lambda \\right)}\\right)^{2}}{\\left(2 M - r{\\left(\\lambda \\right)}\\right) r{\\left(\\lambda \\right)}} + \\left(- 2 M + r{\\left(\\lambda \\right)}\\right) \\left(\\frac{d}{d \\lambda} \\phi{\\left(\\lambda \\right)}\\right)^{2}$"
],
"text/plain": [
" 2 ↪\n",
" ⎛ d ⎞ ⎛ ↪\n",
" 2 M⋅(2⋅M - r(\\lambda))⋅⎜────────(t(\\lambda))⎟ M⋅⎜── ↪\n",
" d ⎝d\\lambda ⎠ ⎝d\\ ↪\n",
"─────────(r(\\lambda)) = ──────────────────────────────────────────── - ─────── ↪\n",
" 2 3 (2⋅M - ↪\n",
"d\\lambda r (\\lambda) ↪\n",
"\n",
"↪ 2 \n",
"↪ d ⎞ \n",
"↪ ──────(r(\\lambda))⎟ 2\n",
"↪ lambda ⎠ ⎛ d ⎞ \n",
"↪ ────────────────────── + (-2⋅M + r(\\lambda))⋅⎜────────(\\phi(\\lambda))⎟ \n",
"↪ r(\\lambda))⋅r(\\lambda) ⎝d\\lambda ⎠ \n",
"↪ "
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gl_c = collect(collect(collect(GeodEq1_a.rhs.expand(),dot[0]),dot[1]),dot[3])\n",
"c0 = simplify(gl_c.coeff(dot[0], 2))\n",
"c1 = simplify(gl_c.coeff(dot[1], 2))\n",
"c3 = simplify(gl_c.coeff(dot[3], 2))\n",
"\n",
"GeodEq1_a_col = Eq(ddot[1],c0*dot[0]**2 + c1*dot[1]**2 + c3*dot[3]**2)\n",
"GeodEq1_a_col"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Um dieses System von drei gekoppelten Differenzialgleichungen zweiter Ordnung mit Python nummerisch lösen zu können, müssen wir es zunächst in ein System von sechs Differenzialgleichungen erster Ordnung umschreiben. Details zur numerischen Lösung von Differenzialgleichungen finden Sie in der Vorlesung Einführung in die Programmierung für Studierende der Physik in den Unterpunkten Differenzialgleichungen: Numerische Lösung von Anfangswertproblemen und \n",
"Systeme von gekoppelten Differenzialgleichungen und Differenzialgleichungen zweiter Ordnung.\n",
"\n",
"Wir definieren dazu formal\n",
"\n",
"$$\n",
"t(\\tau) = y_1(\\tau) \\, , \\quad r(\\tau) = y_2(\\tau), \\quad \\phi(\\tau) = y_3(\\tau) \\, , \\quad \\frac{d t(\\tau)}{d\\tau} = y_4(\\tau) \\, , \\quad \\frac{d r(\\tau)}{d\\tau} = y_5(\\tau), \\quad \\frac{d \\phi(\\tau)}{d\\tau} = y_6\n",
"$$\n",
"\n",
"und schreiben unser DGL-System wie folgt um:\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"y1, y2, y3, y4, y5, y6 = symbols('y_1, y_2, y_3, y_4, y_5, y_6')"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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AZ+Gu3xyaBNjf3ESDutZ96ffpSdlIUyjt4gDiVs+jIBrSPNI+PPApwuIy9rJEppZCO7n2iHa4ywuvyPurlyp5H8X+Jzl8YujC7fpBAPtz9lpz35PR/bHDGjImuxhkCH2PduxLZYHxy1iJaO5j3wXYnSwLyRGnyGdqg73x/wEcPDfhuovuGQAAAABJRU5ErkJggg==",
"text/latex": [
"$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} t{\\left(\\lambda \\right)} = \\frac{2 M y_{4} y_{5}}{y_{2} \\left(2 M - y_{2}\\right)}$"
],
"text/plain": [
" 2 \n",
" d 2⋅M⋅y₄⋅y₅ \n",
"─────────(t(\\lambda)) = ─────────────\n",
" 2 y₂⋅(2⋅M - y₂)\n",
"d\\lambda "
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"SysDGL_0 = Eq(ddot[0],GeodEq0_a.rhs.subs({(param[1],y2),(param[3],y3),(dot[0],y4),(dot[1],y5),(dot[3],y6)}))\n",
"SysDGL_0"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/latex": [
"$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} r{\\left(\\lambda \\right)} = - \\frac{M y_{5}^{2}}{y_{2} \\left(2 M - y_{2}\\right)} + \\frac{M y_{4}^{2} \\left(2 M - y_{2}\\right)}{y_{2}^{3}} + y_{6}^{2} \\left(- 2 M + y_{2}\\right)$"
],
"text/plain": [
" 2 2 2 \n",
" d M⋅y₅ M⋅y₄ ⋅(2⋅M - y₂) 2 \n",
"─────────(r(\\lambda)) = - ───────────── + ──────────────── + y₆ ⋅(-2⋅M + y₂)\n",
" 2 y₂⋅(2⋅M - y₂) 3 \n",
"d\\lambda y₂ "
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"SysDGL_1 = Eq(ddot[1],GeodEq1_a_col.rhs.subs({(param[1],y2),(param[3],y3),(dot[0],y4),(dot[1],y5),(dot[3],y6)}))\n",
"SysDGL_1"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
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"text/latex": [
"$\\displaystyle \\frac{d^{2}}{d \\lambda^{2}} \\phi{\\left(\\lambda \\right)} = - \\frac{2 y_{5} y_{6}}{y_{2}}$"
],
"text/plain": [
" 2 \n",
" d -2⋅y₅⋅y₆ \n",
"─────────(\\phi(\\lambda)) = ─────────\n",
" 2 y₂ \n",
"d\\lambda "
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"SysDGL_3 = Eq(ddot[3],GeodEq3_a.rhs.subs({(param[1],y2),(param[3],y3),(dot[0],y4),(dot[1],y5),(dot[3],y6)}))\n",
"SysDGL_3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Dieses System von drei gekoppelten DGLs 2. Ordnung in der Eigenzeit $\\tau$ 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": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"wert = 2*M*y_4*y_5/(y_2*(2*M - y_2));\n",
"wert = -M*pow(y_5, 2)/(y_2*(2*M - y_2)) + M*pow(y_4, 2)*(2*M - y_2)/pow(y_2, 3) + pow(y_6, 2)*(-2*M + y_2);\n",
"wert = -2*y_5*y_6/y_2;\n"
]
}
],
"source": [
"from sympy.codegen.ast import Assignment\n",
"\n",
"wert = symbols('wert')\n",
"print(ccode(Assignment(wert,SysDGL_0.rhs)))\n",
"print(ccode(Assignment(wert,SysDGL_1.rhs)))\n",
"print(ccode(Assignment(wert,SysDGL_3.rhs)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nun lösen wir die DGLs mittels Python und setzen im Folgenden $M=1$. Wir benutzen hierfür das Python-Modul SciPy, welches eine breite Kollektion von mathematischen Algorithmen und Funktionen bereitstellt. Im Speziellen werden wir in diesem Semester die Funktion 'solve_ivp(...)' verwenden, die sich im Untermodul 'scipy.integrate' 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": 18,
"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 sechs Differenzialgleichungen:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"set_M = 1\n",
"f_4 = lambdify((y1,y2,y3,y4,y5,y6), SysDGL_0.rhs.subs(M,set_M))\n",
"f_5 = lambdify((y1,y2,y3,y4,y5,y6), SysDGL_1.rhs.subs(M,set_M))\n",
"f_6 = lambdify((y1,y2,y3,y4,y5,y6), SysDGL_3.rhs.subs(M,set_M))"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"def DGLsys(vy, time):\n",
" y1,y2,y3,y4,y5,y6 = vy\n",
" dy1 = y4\n",
" dy2 = y5\n",
" dy3 = y6\n",
" dy4 = f_4(y1,y2,y3,y4,y5,y6)\n",
" dy5 = f_5(y1,y2,y3,y4,y5,y6)\n",
" dy6 = f_6(y1,y2,y3,y4,y5,y6)\n",
" return np.array([dy1,dy2,dy3,dy4,dy5,dy6])"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"def DGLsys_ivp(time, vy):\n",
" y1,y2,y3,y4,y5,y6 = vy\n",
" dy1 = y4\n",
" dy2 = y5\n",
" dy3 = y6\n",
" dy4 = f_4(y1,y2,y3,y4,y5,y6)\n",
" dy5 = f_5(y1,y2,y3,y4,y5,y6)\n",
" dy6 = f_6(y1,y2,y3,y4,y5,y6)\n",
" return np.array([dy1,dy2,dy3,dy4,dy5,dy6])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In Abhängigkeit von den Anfangswerten können unterschiedliche Bahnen der Bewegung entstehen. Wir wählen zunächst als Beispiel einer gebundenen elliptischen Bahn. Zur Zeit $t=\\tau=0$ befindet sich der Probekörper bei einem Radius von $r_0=10=5 R_S$ und Winkel $\\phi_0=0$. Seine Anfangsgeschwindigkeit in radialer Richtung sei $\\left. \\frac{dr}{d\\tau} \\right|_{\\tau=0}=0$ und seine Anfangsgeschwindigkeit in $\\phi$-Richtung sei $\\left. \\frac{dr}{d\\tau} \\right|_{\\tau=0}=0.041$. 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). "
]
},
{
"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": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/latex": [
"$\\displaystyle - \\mathrm{d}\\phi^{2} r^{2} \\sin^{2}{\\left(\\theta \\right)} - \\mathrm{d}\\theta^{2} r^{2} - \\frac{\\mathrm{d}r^{2}}{- \\frac{2 M}{r} + 1} + \\mathrm{d}t^{2} \\left(- \\frac{2 M}{r} + 1\\right) = 1$"
],
"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⎟ = 1\n",
"↪ ⎝ r ⎠ \n",
"↪ \n",
"↪ "
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ds2 = g.line_element()\n",
"Eq_ds = Eq(ds2,1)\n",
"Eq_ds"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Umbenennung der Symbole"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"ds_symb = list(ds2.free_symbols)\n",
"for s in ds_symb:\n",
" if (latex(s)==r\"\\mathrm{d}t\"):\n",
" dt = s\n",
" if (latex(s)==r\"\\mathrm{d}r\"):\n",
" dr = s\n",
" if (latex(s)==r\"\\mathrm{d}\\theta\"):\n",
" dtheta = s\n",
" if (latex(s)==r\"\\mathrm{d}\\phi\"):\n",
" dphi = s "
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/latex": [
"$\\displaystyle - \\mathrm{d}\\phi^{2} r^{2} - \\frac{\\mathrm{d}r^{2}}{- \\frac{2 M}{r} + 1} + \\mathrm{d}t^{2} \\left(- \\frac{2 M}{r} + 1\\right) = 1$"
],
"text/plain": [
" 2 \n",
" 2 2 \\mathrm{d}r 2 ⎛ 2⋅M ⎞ \n",
"- \\mathrm{d}\\phi ⋅r - ──────────── + \\mathrm{d}t ⋅⎜- ─── + 1⎟ = 1\n",
" 2⋅M ⎝ r ⎠ \n",
" - ─── + 1 \n",
" r "
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Eq_ds = Eq_ds.subs({(dtheta,0),(theta,pi/2)})\n",
"Eq_ds"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir lösen diese Gleichung nach $dt$ auf:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/latex": [
"$\\displaystyle \\left[ \\frac{\\sqrt{r} \\sqrt{- 2 M \\mathrm{d}\\phi^{2} r^{2} - 2 M + \\mathrm{d}\\phi^{2} r^{3} + \\mathrm{d}r^{2} r + r}}{- 2 M + r}, \\ \\frac{\\sqrt{r} \\sqrt{- 2 M \\mathrm{d}\\phi^{2} r^{2} - 2 M + \\mathrm{d}\\phi^{2} r^{3} + \\mathrm{d}r^{2} r + r}}{2 M - r}\\right]$"
],
"text/plain": [
"⎡ _______________________________________________________________________ ↪\n",
"⎢ ╱ 2 2 2 3 2 ↪\n",
"⎢√r⋅╲╱ - 2⋅M⋅\\mathrm{d}\\phi ⋅r - 2⋅M + \\mathrm{d}\\phi ⋅r + \\mathrm{d}r ⋅r + ↪\n",
"⎢───────────────────────────────────────────────────────────────────────────── ↪\n",
"⎣ -2⋅M + r ↪\n",
"\n",
"↪ ___ _________________________________________________________________ ↪\n",
"↪ ╱ 2 2 2 3 ↪\n",
"↪ r √r⋅╲╱ - 2⋅M⋅\\mathrm{d}\\phi ⋅r - 2⋅M + \\mathrm{d}\\phi ⋅r + \\mathrm{d} ↪\n",
"↪ ───, ─────────────────────────────────────────────────────────────────────── ↪\n",
"↪ 2⋅M - r ↪\n",
"\n",
"↪ _________⎤\n",
"↪ 2 ⎥\n",
"↪ r ⋅r + r ⎥\n",
"↪ ─────────⎥\n",
"↪ ⎦"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"LoesEq_ds = solve(Eq_ds,dt)\n",
"LoesEq_ds"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir benutzen die erste Lösung (positive Lösung) und berechnen für unsere Anfangsbedingung $\\left. \\frac{dt}{d\\tau} \\right|_{\\tau=0}=1.20835632162041$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Im Folgenden setzen wir die relativen und absoluten Fehler-Toleranzen der Python Simulationen (rtol und atol) auf $10^{-13}$."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"N = 10000\n",
"tauval = np.linspace(0, 800, N+1)\n",
"\n",
"r0 = 10.0\n",
"t0 = 0.0\n",
"phi0 = 0.0\n",
"dr0 = 0.0\n",
"dphi0 = 0.041\n",
"dt0 = float(LoesEq_ds[0].subs({(r,r0),(dr,dr0),(dphi,dphi0),(M,set_M)}))\n",
"\n",
"initialval = np.array([t0,r0,phi0,dt0,dr0,dphi0])\n",
"\n",
"Loes = integrate.odeint(DGLsys, initialval, tauval, rtol=10**(-13), atol=10**(-13))\n",
"Loes_ivp = integrate.solve_ivp(DGLsys_ivp, [tauval[0], tauval[-1]], initialval, t_eval=tauval, rtol=10**(-13), atol=10**(-13))"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"dt0 = 1.208356321620407\n"
]
}
],
"source": [
"print(\"dt0 =\",dt0)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"rcParams.update({\n",
" 'figure.figsize' : [6,6],\n",
" 'axes.titlesize' : 14,\n",
" 'axes.labelsize' : 16, \n",
" 'xtick.labelsize' : 14 ,\n",
" 'ytick.labelsize' : 14 \n",
"})"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.cla()\n",
"plt.ylabel(r\"$\\rm Radius \\,\\,r \\,[km]$\")\n",
"plt.xlabel(r\"$\\rm Eigenzeit \\,\\,\\tau$\")\n",
"plt.plot(tauval,Loes[:, 1],c=\"blue\", linewidth=1.5, linestyle='-');\n",
"plt.plot(Loes_ivp.t,Loes_ivp.y[1],c=\"red\", linewidth=2, linestyle=':');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Das obere Diagramm zeigt den Abstand des Probekörpers vom schwarzen Loch (Radius r) als Funktion der Eigenzeit $\\tau$, wobei die blaue Kurve die Ergebnisse der odeint-Methode und die gepunktete rote Kurve die solve_ivp-Simulation zeigt. Beide Simulationen stimmen gut miteinander überein. Am Ende der Simulation ergeben sich die folgenden Werte für $(t,r,\\phi,\\frac{d t(\\tau)}{d\\tau},\\frac{d r(\\tau)}{d\\tau},\\frac{d \\phi(\\tau)}{d\\tau})$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"solve_ivp-Methode:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"908.6596298577555 11.037946990240393 18.670947098352382 1.1806020139548372 0.05196781454255374 0.03365171860146632\n"
]
}
],
"source": [
"print(Loes_ivp.y[0][-1],Loes_ivp.y[1][-1],Loes_ivp.y[2][-1],Loes_ivp.y[3][-1],Loes_ivp.y[4][-1],Loes_ivp.y[5][-1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"odeint-Methode:"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"908.6596298639798 11.037946990052614 18.67094709978148 1.1806020139578826 0.05196781457288299 0.03365171860164547\n"
]
}
],
"source": [
"print(Loes[-1, 0],Loes[-1, 1],Loes[-1, 2],Loes[-1, 3],Loes[-1, 4],Loes[-1, 5])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Die Trajektorie des Körpers wird in dem unteren Bild dargestellt, wobei der rote Punkt den Anfangsort des Probekörpers zeigt."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = plt.gca()\n",
"ax.cla() \n",
"ax.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
"ax.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
"ax.plot(Loes[:, 1]*np.cos(Loes[:, 2]),Loes[:, 1]*np.sin(Loes[:, 2]),c=\"blue\", linewidth=1.5, linestyle='-');\n",
"ax.scatter(Loes[0, 1]*np.cos(Loes[0, 2]),Loes[0, 1]*np.sin(Loes[0, 2]),c=\"red\", s=60, marker='o');\n",
"BH = plt.Circle((0, 0), 2, color='black')\n",
"ax.add_patch(BH);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir werden in Kürze sehen, dass es Erhaltungsgrößen während der Bewegung des Probekörpers gibt. Während der gesamten Bewegung wird der Drehimpuls $l$ pro Masse $m$, die Teilchenenergie $e$ pro Masse und das Weglängenelement $ds^2$ erhalten. In der numerischen Simulation sind diese Größen ebenfalls in Näherung erhalten, wie man in den folgenden Abbildungen sieht (hier für die odeint-Simulation dargestellt)."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.gridspec as gridspec"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(16,5))\n",
"gs = gridspec.GridSpec(1, 3, width_ratios=[1,1,1], wspace=0.25)\n",
"ax1 = plt.subplot(gs[0])\n",
"ax2 = plt.subplot(gs[1])\n",
"ax3 = plt.subplot(gs[2])\n",
"\n",
"ax1.set_ylabel(r\"$\\rm Drehimpuls \\,\\,l$\")\n",
"ax1.set_xlabel(r\"$\\rm Eigenzeit \\,\\,\\tau$\")\n",
"ax2.set_ylabel(r\"$\\rm Energie \\,\\,e $\")\n",
"ax2.set_xlabel(r\"$\\rm Eigenzeit \\,\\,\\tau$\")\n",
"ax3.set_ylabel(r\"$\\rm Weglaengenelement \\,\\,ds^2$\")\n",
"ax3.set_xlabel(r\"$\\rm Eigenzeit \\,\\,\\tau$\")\n",
"\n",
"data_l = Loes[:, 1]**2*Loes[:, 5]\n",
"data_E = (1-2/Loes[:, 1])*Loes[:, 3]\n",
"data_ds2 = (1-2/Loes[:, 1])*Loes[:, 3]**2-Loes[:, 4]**2/(1-2/Loes[:, 1])-Loes[:, 5]**2*Loes[:, 1]**2\n",
"\n",
"ax1.plot(tauval,data_l,c=\"blue\", linewidth=1.5, linestyle='-');\n",
"ax2.plot(tauval,data_E,c=\"blue\", linewidth=1.5, linestyle='-');\n",
"ax3.plot(tauval,data_ds2,c=\"blue\", linewidth=1.5, linestyle='-');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir vergleichen nun die Ergebnisse mit dem C++ Programm aus Vorlesung 6. Bei der Erzeugung der Daten wurden $N=100000$ Gitterpunkten verwendet und die Ergebnisse des C++ Programms wurden in die Datei geodesic.dat geschrieben.\n",
"\n",
"Um das Jupyter Notebook fehlerfrei weiter ausführen zu können, müssen Sie die Ausgabedatei geodesic.dat des C++ Programms (GeodesicSchwarzschild.cpp und GeodesicSchwarzschild.hpp) in demselben Verzeichnis haben, in dem Sie dieses Jupyter Notebook gestartet haben. "
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"data = np.genfromtxt(\"./geodesic.dat\")"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"rcParams.update({\n",
" 'figure.figsize' : [11,10],\n",
" 'axes.titlesize' : 14,\n",
" 'axes.labelsize' : 16, \n",
" 'xtick.labelsize' : 14 ,\n",
" 'ytick.labelsize' : 14 \n",
"})"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure() # Hauptbild\n",
"gs = gridspec.GridSpec(2, 2, width_ratios=[1,1], wspace=0.3, hspace=0.3) # Anordnung der vier Unterbilder\n",
"ax1 = plt.subplot(gs[0])\n",
"ax2 = plt.subplot(gs[1])\n",
"ax3 = plt.subplot(gs[2])\n",
"ax4 = plt.subplot(gs[3])\n",
"\n",
"ax1.set_title(r'Koordinatenzeit t') # Titel der Abbildung in ax1\n",
"ax1.set_xlabel(r\"$\\rm \\tau$\")\n",
"ax1.set_ylabel(r\"$\\rm t$\")\n",
"ax2.set_title(r'Radius r') # Titel der Abbildung in ax2 \n",
"ax2.set_xlabel(r\"$\\rm \\tau$\")\n",
"ax2.set_ylabel(r\"$\\rm r$\")\n",
"ax3.set_title(r'Winkel') # Titel der Abbildung in ax3 \n",
"ax3.set_xlabel(r\"$\\rm \\tau$\")\n",
"ax3.set_ylabel(r\"$\\rm \\phi$\")\n",
"ax4.set_title(r'Trajektorie') # Titel der Abbildung in ax4 \n",
"ax4.set_xlabel(r\"$\\rm x$\")\n",
"ax4.set_ylabel(r\"$\\rm y$\")\n",
"\n",
"l_width = 0.8 # Festlegung der Plot-Liniendicke \n",
"alp = 0.7 # Festlegung der Transparenz der Kurven\n",
"\n",
"ax1.plot(data[:,1],data[:,2], color=\"red\", linewidth=l_width, linestyle='-', alpha=alp, label=r'$\\rm C++-RK4$')\n",
"ax1.plot(Loes_ivp.t,Loes_ivp.y[0], color=\"blue\", linewidth=l_width, linestyle='-', alpha=alp, label=r'$\\rm Python-ivp$')\n",
"ax1.plot(tauval, Loes[:, 0],c=\"green\", linewidth=l_width, linestyle='-', alpha=alp, label=r\"$\\rm Python-odeint$\")\n",
"\n",
"ax2.plot(data[:,1],data[:,3], color=\"red\", linewidth=l_width, linestyle='-', alpha=alp, label=r'$\\rm C++-RK4$')\n",
"ax2.plot(Loes_ivp.t,Loes_ivp.y[1], color=\"blue\", linewidth=l_width, linestyle='-', alpha=alp, label=r'$\\rm Python-ivp$')\n",
"ax2.plot(tauval, Loes[:, 1],c=\"green\", linewidth=l_width, linestyle='-', alpha=alp, label=r\"$\\rm Python-odeint$\")\n",
"\n",
"ax3.plot(data[:,1],data[:,4], color=\"red\", linewidth=l_width, linestyle='-', alpha=alp, label=r'$\\rm C++-RK4$')\n",
"ax3.plot(Loes_ivp.t,Loes_ivp.y[2], color=\"blue\", linewidth=l_width, linestyle='-', alpha=alp, label=r'$\\rm Python-ivp$')\n",
"ax3.plot(tauval, Loes[:, 2],c=\"green\", linewidth=l_width, linestyle='-', alpha=alp, label=r\"$\\rm Python-odeint$\")\n",
"\n",
"ax4.plot(data[:, 3]*np.cos(data[:, 4]),data[:, 3]*np.sin(data[:, 4]),c=\"red\", linewidth=1.5, linestyle='-', label=r'$\\rm C++-RK4$');\n",
"ax4.plot(Loes_ivp.y[1]*np.cos(Loes_ivp.y[2]),Loes_ivp.y[1]*np.sin(Loes_ivp.y[2]),c=\"blue\", linewidth=1.5, linestyle='-', label=r'$\\rm Python-ivp$')\n",
"ax4.plot(Loes[:, 1]*np.cos(Loes[:, 2]),Loes[:, 1]*np.sin(Loes[:, 2]),c=\"green\", linewidth=1.5, linestyle='-', label=r\"$\\rm odeint$\")\n",
"ax4.scatter(Loes[0, 1]*np.cos(Loes[0, 2]),Loes[0, 1]*np.sin(Loes[0, 2]),c=\"green\", s=60, marker='o')\n",
"\n",
"ax1.legend(frameon=True, loc=\"upper left\",fontsize=12) \n",
"ax2.legend(frameon=True, loc=\"upper left\",fontsize=12)\n",
"ax3.legend(frameon=True, loc=\"upper left\",fontsize=12) \n",
"ax4.legend(frameon=True, loc=\"upper left\",fontsize=12);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Die oberen Abbildungen zeigen, dass die Resultate des C++ Programms gut mit den Ergebnissen der Python Simulationen übereinstimmen. Um dies genauer zu analysieren, stellen wir in der folgenden Grafik die Abweichungen der Python Simulationen von der C++ Lösung dar ($\\Delta t$, $\\Delta r$ und $\\Delta \\phi$) und Vergleichen die Erhaltung der Energie zwischen den Simulationen."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
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",
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""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure() # Hauptbild\n",
"gs = gridspec.GridSpec(2, 2, width_ratios=[1,1], wspace=0.3, hspace=0.3) # Anordnung der vier Unterbilder\n",
"ax1 = plt.subplot(gs[0])\n",
"ax2 = plt.subplot(gs[1])\n",
"ax3 = plt.subplot(gs[2])\n",
"ax4 = plt.subplot(gs[3])\n",
"\n",
"ax1.set_title(r'Abweichungen Koordinatenzeit t') # Titel der Abbildung in ax1\n",
"ax1.set_xlabel(r\"$\\rm \\tau$\")\n",
"ax1.set_ylabel(r\"$\\rm \\Delta t$\")\n",
"ax2.set_title(r'Abweichungen Radius r') # Titel der Abbildung in ax2 \n",
"ax2.set_xlabel(r\"$\\rm \\tau$\")\n",
"ax2.set_ylabel(r\"$\\rm \\Delta r$\")\n",
"ax3.set_title(r'Abweichungen Winkel') # Titel der Abbildung in ax3 \n",
"ax3.set_xlabel(r\"$\\rm \\tau$\")\n",
"ax3.set_ylabel(r\"$\\rm \\Delta \\phi$\")\n",
"ax4.set_title(r'Energie Erhaltung') # Titel der Abbildung in ax4 \n",
"ax4.set_ylabel(r\"$\\rm Energie \\,\\,e $\")\n",
"ax4.set_xlabel(r\"$\\rm \\tau$\")\n",
"\n",
"l_width = 0.8 # Festlegung der Plot-Liniendicke \n",
"alp = 0.7 # Festlegung der Transparenz der Kurven\n",
"\n",
"ax1.plot(Loes_ivp.t,Loes_ivp.y[0]-data[:,2], color=\"blue\", linewidth=l_width, linestyle='-', alpha=alp, label='RK4 vs. ivp') \n",
"ax1.plot(tauval, Loes[:, 0]-data[:,2],c=\"green\", linewidth=l_width, linestyle='-', alpha=alp, label='RK4 vs. odeint')\n",
"\n",
"ax2.plot(Loes_ivp.t,Loes_ivp.y[1]-data[:,3], color=\"blue\", linewidth=l_width, linestyle='-', alpha=alp, label='RK4 vs. ivp')\n",
"ax2.plot(tauval, Loes[:, 1]-data[:,3],c=\"green\", linewidth=l_width, linestyle='-', alpha=alp, label='RK4 vs. odeint')\n",
"\n",
"ax3.plot(Loes_ivp.t,Loes_ivp.y[2]-data[:,4], color=\"blue\", linewidth=l_width, linestyle='-', alpha=alp, label='RK4 vs. ivp')\n",
"ax3.plot(tauval, Loes[:, 2]-data[:,4],c=\"green\", linewidth=l_width, linestyle='-', alpha=alp, label='RK4 vs. odeint')\n",
"\n",
"ax4.plot(data[:,1],(1-2/data[:,3])*data[:,5],c=\"red\", linewidth=1.5, linestyle='-', label=r'$\\rm C++-RK4$');\n",
"ax4.plot(Loes_ivp.t,(1-2/Loes_ivp.y[1])*Loes_ivp.y[3],c=\"blue\", linewidth=1.5, linestyle='-', label=r'$\\rm Python-ivp$')\n",
"ax4.plot(tauval,(1-2/Loes[:, 1])*Loes[:, 3],c=\"green\", linewidth=1.5, linestyle='-', label=r\"$\\rm odeint$\")\n",
"\n",
"ax1.legend(frameon=True, loc=\"upper left\",fontsize=12) \n",
"ax2.legend(frameon=True, loc=\"upper left\",fontsize=12)\n",
"ax3.legend(frameon=True, loc=\"upper left\",fontsize=12) \n",
"ax4.legend(frameon=True, loc=\"lower right\",fontsize=12);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Klassifizierung unterschiedlicher Bahnbewegungen\n",
"\n",
"Literatur:\n",
"\n",
"\n",
" - General relativity : An introduction for physicists von M. P. Hobson, G. P. Efstathiou und A. N. Lasenby
\n",
" - Gravity : An introduction to Einstein's general relativity von James B. Hartle
\n",
" - Allgemeine Relativitätstheorie von Torsten Fließbach
\n",
" - Relativistic hydrodynamics von Luciano Rezzolla und Olindo Zanotti
\n",
"
\n",
"\n",
"\n",
"\n",
"Man kann zeigen (siehe z.B. Seite 206 in General relativity : An introduction for physicists by M. P. Hobson, G. P. Efstathiou and A. N. Lasenby), dass sich die erste und vierte Gleichung des Systems der Differenzialgleichungen der Geodätengleichung in die folgenden Gleichungen umschreiben lässt:\n",
"$$\n",
"\\begin{eqnarray}\n",
"\\hbox{1. Gleichung:}&& \\frac{d}{d\\tau} \\left[ \\left( 1 - \\frac{2 M}{r} \\right) \\frac{dt}{d\\tau} \\right] = 0 \\\\\n",
"\\rightarrow && \\left( 1 - \\frac{2 M}{r} \\right) \\frac{dt}{d\\tau} = e = \\hbox{const} \\\\\n",
"\\hbox{4. Gleichung:}&& \\frac{d}{d\\tau} \\left( r^2 \\hbox{sin}^2(\\theta) \\frac{d\\phi}{d\\tau} \\right) = 0 \\\\\n",
"\\rightarrow && r^2 \\hbox{sin}^2(\\theta) \\frac{d\\phi}{d\\tau} = l = \\hbox{const} \\quad ,\n",
"\\end{eqnarray}\n",
"$$\n",
"wobei die während der Bewegungen erhaltenen Größen e (Teilchenenergie pro Masse, $e=\\frac{E}{m}$) und l (Drehimpuls pro Masse m, $l=\\frac{L}{m}$) sich aus der Definition des Viererimpulses $p_\\mu = m \\, u_\\mu = m \\, g_{\\mu\\nu} \\frac{dx^\\nu}{d\\tau} = m \\, \\left( g_{tt} \\, \\frac{dt}{d\\tau}, g_{rr} \\, \\frac{dr}{d\\tau}, g_{\\theta\\theta} \\, \\frac{d\\theta}{d\\tau}, g_{\\phi\\phi} \\, \\frac{d\\phi}{d\\tau} \\right) $ ergeben (Voraussetzung: diagonale Form der Metrik). Für die Schwarzschildmetrik erhält man:\n",
"\n",
"$$\n",
"\\begin{eqnarray}\n",
"&& p_t = p_0 = m \\frac{dx_0}{d\\tau} = m g_{00} \\frac{dx^0}{d\\tau} = m g_{00} \\frac{dt}{d\\tau} = m \\left( 1 - \\frac{2 M}{r} \\right) \\frac{dt}{d\\tau} = m \\, e \\\\\n",
"&& p_\\phi = p_3 = m \\frac{dx_3}{d\\tau} = m g_{33} \\frac{dx^3}{d\\tau} = m g_{33} \\frac{d\\phi}{d\\tau} = - m \\left( r^2 \\hbox{sin}^2(\\theta) \\right) \\frac{d\\phi}{d\\tau} = - m \\, l\n",
"\\end{eqnarray}\n",
"$$\n",
"\n",
"Die Klassifikation möglicher Bahnen von Probekörpern in vorgegebener Schwarzschild-Raumzeit kann mittels eines definierten effektiven Potenzials illustriert werden. Dieses Potenzial hängt von dem, bei der Bewegung erhaltenen Drehimpuls pro Masse m ab. Die im Zentralfeld möglichen Bewegungen werden mittels zweier erhaltener Größen (l: Drehimpuls pro Masse m und e: Energie pro Masse) charakterisiert. Die Definition des effektiven Potenzial erfolgt mittels der radialen, 2. Geodätengleichung. So definieren z.B. die Literaturangaben 1-3 (siehe Angaben oben) das effektive Potenzial wie folgt:\n",
"$$\n",
"\\begin{eqnarray}\n",
"\\hbox{2. Gleichung:}&\\rightarrow&\\frac{1}{2} \\left( \\frac{dr}{d\\tau} \\right)^2 + V(r,M,l) = \\frac{1}{2} \\left( e^2 -1 \\right) \\\\\n",
"\\hbox{wobei:} && V(r,M,l) = \\frac{l^2}{2 r^2} \\left( 1 - \\frac{2 M}{r} \\right) - \\frac{M}{r} \\quad .\n",
"\\end{eqnarray}\n",
"$$\n",
"In der Literaturangabe 4 wird das Pozential V(r,M,l) hingegen wie folgt definiert:\n",
"\n",
"$$\n",
"\\begin{eqnarray}\n",
"\\hbox{2. Gleichung:}&\\rightarrow& \\left( \\frac{dr}{d\\tau} \\right)^2 + \\left( V(r,M,l) \\right)^2 = e^2 \\\\\n",
"\\hbox{wobei:} && V(r,M,l) = \\sqrt{ \\left( 1 - \\frac{2 M}{r} \\right) \\left( 1 + \\frac{l^2}{r^2} \\right) } \\quad .\n",
"\\end{eqnarray}\n",
"$$ "
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"l = symbols('l')\n",
"VeffFb = -M/r+l**2/(2*r**2)-M*l**2/r**3\n",
"VeffRez = sqrt(1-2*M/r)*sqrt(1+l**2/r**2)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Drehimpuls l\n",
"4.1000000000000005\n",
"Energie e\n",
"0.9666850572963256\n"
]
}
],
"source": [
"setl = r0**2*dphi0\n",
"setE = dt0*((1-2*set_M/r0))\n",
"print(\"Drehimpuls l\")\n",
"print(setl)\n",
"print(\"Energie e\")\n",
"print(setE)\n",
"VeffFbl = lambdify((r),VeffFb.subs({(l,setl),(M,set_M)}))\n",
"VeffRezl = lambdify((r),VeffRez.subs({(l,setl),(M,set_M)}))\n",
"rval = np.linspace(2.85,30, 1001)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(16,8))\n",
"gs = gridspec.GridSpec(1, 2, width_ratios=[1,1], wspace=0.21)\n",
"ax1 = plt.subplot(gs[0])\n",
"ax2 = plt.subplot(gs[1])\n",
"ax1.set_ylabel(r\"$\\rm V_1(r)$\")\n",
"ax1.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
"ax2.set_ylabel(r\"$\\rm V_2(r)$\")\n",
"ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
"ax1.plot(rval,VeffRezl(rval),c=\"blue\", linewidth=1.5, linestyle='-');\n",
"ax2.plot(rval,VeffFbl(rval),c=\"red\", linewidth=1.5, linestyle='-');\n",
"\n",
"ax1.scatter(r0,VeffRezl(r0),c=\"black\", s=80, marker='o');\n",
"ax2.scatter(r0,VeffFbl(r0),c=\"black\", s=80, marker='o');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Die obere Abbildung zeigt (in der Nomenklatur des 4.Buches (Diagramm links) bzw. des 1. bis 3. Buches (Diagramm rechts) ) das effektive Potenzial als Funktion des Radius bei den zuvor gewählten Anfangswerten (schwarze Punkte auf den Kurven).\n",
"\n",
"Wir wollen uns nun die Bewegung des Probekörpers in einer Animation darstellen:"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.animation as animation\n",
"from IPython.display import HTML"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"anzframes = 100\n",
"step = int(N/anzframes-1) \n",
"xylim = 18\n",
"\n",
"fig = plt.figure(figsize=(11, 5))\n",
"gs = gridspec.GridSpec(1, 2, width_ratios=[1,1], wspace=0.3)\n",
"ax1 = plt.subplot(gs[0])\n",
"ax2 = plt.subplot(gs[1])\n",
"\n",
"def init():\n",
" ax1.scatter(Loes[0, 1]*np.cos(Loes[0, 2]),Loes[0, 1]*np.sin(Loes[0, 2]),c=\"red\", s=60, marker='o');\n",
" BH = plt.Circle((0, 0), 2, color='black')\n",
" ax1.add_patch(BH);\n",
" ax2.plot(rval,VeffRezl(rval),c=\"blue\", linewidth=1.5, linestyle='-');\n",
" ax2.scatter(r0,VeffRezl(r0),c=\"red\", s=80, marker='o');\n",
" ax1.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
" ax1.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
" ax2.set_ylabel(r\"$\\rm V(r)$\")\n",
" ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
" ax1.set_xlim(-xylim, xylim)\n",
" ax1.set_ylim(-xylim, xylim)\n",
" return fig,\n",
"\n",
"def animate(i):\n",
" ax1.cla() \n",
" ax2.cla() \n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),c=\"blue\", linewidth=0.5, linestyle='-');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),c=\"red\", s=60, marker='o');\n",
" ax2.plot(rval,VeffRezl(rval),c=\"blue\", linewidth=1.5, linestyle='-');\n",
" ax2.scatter(Loes[step*i, 1],VeffRezl(r0),c=\"red\", s=80, marker='o');\n",
" BH = plt.Circle((0, 0), 2, color='black')\n",
" ax1.add_patch(BH);\n",
" ax1.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
" ax1.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
" ax2.set_ylabel(r\"$\\rm V(r)$\")\n",
" ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
" ax1.set_xlim(-xylim, xylim)\n",
" ax1.set_ylim(-xylim, xylim)\n",
" return fig,\n",
"\n",
"ani = animation.FuncAnimation(fig,animate,init_func=init,frames=anzframes,interval=100)\n",
"plt.close(fig)\n",
"HTML(ani.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"bzw. ohne Verwendung von ax1.cla() und ax2.cla() in jedem Animationsschritt und mit einer Trennung von Animationsobjekten und statischen Elementen."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"anzframes = 100\n",
"step = int(N/anzframes-1) \n",
"\n",
"# Figure-Setup\n",
"fig = plt.figure(figsize=(11, 5))\n",
"gs = gridspec.GridSpec(1, 2, width_ratios=[1, 1], wspace=0.3)\n",
"ax1 = plt.subplot(gs[0])\n",
"ax2 = plt.subplot(gs[1])\n",
"\n",
"# Statische Elemente der Animation\n",
"ax1.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
"ax1.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
"ax1.set_xlim(-xylim, xylim)\n",
"ax1.set_ylim(-xylim, xylim)\n",
"ax2.set_ylabel(r\"$\\rm V(r)$\")\n",
"ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
"# Statische Potentialkurve\n",
"ax2.plot(rval, VeffRezl(rval), c=\"blue\", linewidth=1.5, linestyle='-')\n",
"# Statisches Schwarzes Loch\n",
"BH = plt.Circle((0, 0), 2, color='black')\n",
"ax1.add_patch(BH)\n",
"\n",
"# Animationsobjekte initialisieren\n",
"line_orbit, = ax1.plot([], [], c=\"blue\", linewidth=0.5, linestyle='-')\n",
"scatter_body = ax1.scatter([], [], c=\"red\", s=60, marker='o')\n",
"scatter_pot = ax2.scatter([], [], c=\"red\", s=80, marker='o')\n",
"\n",
"# Simulationswerte der Trajektorie\n",
"x_all = Loes[:, 1] * np.cos(Loes[:, 2])\n",
"y_all = Loes[:, 1] * np.sin(Loes[:, 2])\n",
"\n",
"def init():\n",
" line_orbit.set_data([], [])\n",
" scatter_body.set_offsets(np.c_[x_all[0], y_all[0]])\n",
" scatter_pot.set_offsets(np.c_[Loes[0, 1], VeffRezl(Loes[0, 1])]) \n",
" return line_orbit, scatter_body, scatter_pot\n",
"\n",
"def animate(i):\n",
" idx = step * i\n",
" line_orbit.set_data(x_all[:idx], y_all[:idx])\n",
" scatter_body.set_offsets(np.c_[x_all[idx], y_all[idx]])\n",
" scatter_pot.set_offsets(np.c_[Loes[idx, 1], VeffRezl(Loes[0, 1])])\n",
" return line_orbit, scatter_body, scatter_pot\n",
"\n",
"ani = animation.FuncAnimation(\n",
" fig, animate, init_func=init, frames=anzframes, \n",
" interval=100, blit=True\n",
")\n",
"\n",
"plt.close(fig)\n",
"HTML(ani.to_html5_video())\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir betrachten uns die gleiche Animation in einem eingebetteten Diagramm der räumlichen Hypersphäre der Mannigfaltigkeit:"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [],
"source": [
"from mpl_toolkits.mplot3d import Axes3D\n",
"from matplotlib import cm"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [],
"source": [
"x,y = symbols('x,y')\n",
"zBett = sqrt(8*M*(r-2*M))\n",
"R = np.linspace(2.00001, 20, 300)\n",
"PHI = np.linspace(0, 2*np.pi, 300)\n",
"R, PHI = np.meshgrid(R, PHI)\n",
"X = R*np.cos(PHI)\n",
"Y = R*np.sin(PHI)\n",
"zlam = lambdify((x,y), zBett.subs({(M,set_M),(r,sqrt(x**2+y**2))}))\n",
"ZF = np.array(list(np.real(zlam(X,Y))))"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"anzframes = 50\n",
"step = int(N/anzframes-1) \n",
"xylim = 18\n",
"zlim = 15\n",
"fig = plt.figure(figsize=(11,5))\n",
"gs = gridspec.GridSpec(1, 2, width_ratios=[2,1], wspace=0.21)\n",
"ax1 = plt.subplot(gs[0],projection='3d')\n",
"ax2 = plt.subplot(gs[1])\n",
"ax1.xaxis.pane.fill = False\n",
"ax1.yaxis.pane.fill = False\n",
"ax1.zaxis.pane.fill = False\n",
"ax1.xaxis.pane.set_edgecolor('white')\n",
"ax1.yaxis.pane.set_edgecolor('white')\n",
"ax1.zaxis.pane.set_edgecolor('white')\n",
"\n",
"def init():\n",
" ax1.plot_surface(X, Y, ZF, cmap=cm.nipy_spectral, linewidth=0, alpha=0.5)\n",
" ax1.scatter(Loes[0, 1]*np.cos(Loes[0, 2]),Loes[0, 1]*np.sin(Loes[0, 2]),np.real(zlam(Loes[0, 1]*np.cos(Loes[0, 2]),Loes[0, 1]*np.sin(Loes[0, 2]))),c=\"black\", s=60, marker='o');\n",
" ax1.contourf(X, Y, ZF,100, zdir='z', offset=0, cmap=cm.nipy_spectral,alpha=0.5)\n",
" ax1.scatter(Loes[0, 1]*np.cos(Loes[0, 2]),Loes[0, 1]*np.sin(Loes[0, 2]),0.1,c=\"black\", s=40, marker='o');\n",
" ax2.plot(rval,VeffRezl(rval),c=\"black\", linewidth=1.5, linestyle='-');\n",
" ax2.scatter(r0,VeffRezl(r0),c=\"black\", s=80, marker='o');\n",
" ax1.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
" ax1.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
" ax1.set_zlabel(\"Visualisierung z\");\n",
" ax2.set_ylabel(r\"$\\rm V(r)$\")\n",
" ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
" ax1.view_init(azim=35, elev=20)\n",
" ax1.set_xlim(-xylim, xylim)\n",
" ax1.set_ylim(-xylim, xylim)\n",
" ax1.set_zlim(0, 15)\n",
" ax1.grid(False)\n",
" return fig,\n",
"\n",
"def animate(i):\n",
" ax1.cla() \n",
" ax2.cla()\n",
" ax1.plot_surface(X, Y, ZF, cmap=cm.nipy_spectral, linewidth=0, alpha=0.5)\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),np.real(zlam(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]))),c=\"black\", linewidth=1, linestyle='-');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),np.real(zlam(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]))),c=\"black\", s=60, marker='o');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),0.1,c=\"black\", s=40, marker='o');\n",
" ax1.contourf(X, Y, ZF,100, zdir='z', offset=0, cmap=cm.nipy_spectral,alpha=0.5)\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),0.1,c=\"black\", linewidth=2.5, linestyle='-');\n",
" ax2.plot(rval,VeffRezl(rval),c=\"black\", linewidth=1.5, linestyle='-');\n",
" ax2.scatter(Loes[step*i, 1],VeffRezl(r0),c=\"black\", s=80, marker='o');\n",
" ax1.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
" ax1.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
" ax1.set_zlabel(\"Einbettung z\");\n",
" ax2.set_ylabel(r\"$\\rm V(r)$\")\n",
" ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
" ax1.view_init(azim=35, elev=20)\n",
" ax1.set_xlim(-xylim, xylim)\n",
" ax1.set_ylim(-xylim, xylim)\n",
" ax1.set_zlim(0, 15) \n",
" ax1.grid(False)\n",
" return fig,\n",
"\n",
"ani = animation.FuncAnimation(fig,animate,init_func=init,frames=anzframes,interval=100)\n",
"plt.close(fig)\n",
"HTML(ani.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"bzw. ohne Verwendung von ax1.cla() und ax2.cla() in jedem Animationsschritt und mit einer Trennung von Animationsobjekten und statischen Elementen."
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"anzframes = 50\n",
"step = int(N/anzframes-1) \n",
"xylim = 18\n",
"zlim = 15\n",
"\n",
"# Figure-Setup\n",
"fig = plt.figure(figsize=(11, 5))\n",
"gs = gridspec.GridSpec(1, 2, width_ratios=[2, 1], wspace=0.21)\n",
"ax1 = plt.subplot(gs[0], projection='3d')\n",
"ax2 = plt.subplot(gs[1])\n",
"\n",
"for axis in [ax1.xaxis, ax1.yaxis, ax1.zaxis]:\n",
" axis.pane.fill = False\n",
" axis.pane.set_edgecolor('white')\n",
"\n",
"# Achsen-Konfiguration\n",
"ax1.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
"ax1.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
"ax1.set_zlabel(\"Einbettung z\")\n",
"ax1.set_xlim(-xylim, xylim)\n",
"ax1.set_ylim(-xylim, xylim)\n",
"ax1.set_zlim(0, zlim)\n",
"ax1.view_init(azim=35, elev=20)\n",
"ax1.grid(False)\n",
"ax2.set_ylabel(r\"$\\rm V(r)$\")\n",
"ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
"\n",
"ax1.plot_surface(X, Y, ZF, cmap=cm.nipy_spectral, linewidth=0, alpha=0.5)\n",
"ax1.contourf(X, Y, ZF, 100, zdir='z', offset=0, cmap=cm.nipy_spectral, alpha=0.5)\n",
"ax2.plot(rval, VeffRezl(rval), c=\"black\", linewidth=1.5, linestyle='-')\n",
"\n",
"line_3d, = ax1.plot([], [], [], c=\"black\", linewidth=1, linestyle='-') # Trajektorie auf Fläche\n",
"line_shadow, = ax1.plot([], [], [], c=\"black\", linewidth=2.5, linestyle='-') # Schatten auf dem Boden\n",
"\n",
"scatter_3d = ax1.scatter([], [], [], c=\"black\", s=60, marker='o')\n",
"scatter_shadow = ax1.scatter([], [], [], c=\"black\", s=40, marker='o')\n",
"scatter_pot = ax2.scatter([], [], c=\"black\", s=80, marker='o')\n",
"\n",
"x_all = Loes[:, 1] * np.cos(Loes[:, 2])\n",
"y_all = Loes[:, 1] * np.sin(Loes[:, 2])\n",
"z_all = np.real(zlam(x_all, y_all))\n",
"z_shadow = np.full_like(z_all, 0.1) \n",
"\n",
"def init():\n",
" line_3d.set_data([], [])\n",
" line_3d.set_3d_properties([])\n",
" line_shadow.set_data([], [])\n",
" line_shadow.set_3d_properties([])\n",
" \n",
" scatter_3d._offsets3d = ([], [], [])\n",
" scatter_shadow._offsets3d = ([], [], [])\n",
" scatter_pot.set_offsets(np.c_[[], []])\n",
" return fig,\n",
"\n",
"def animate(i):\n",
" idx = step * i\n",
" line_3d.set_data(x_all[:idx], y_all[:idx])\n",
" line_3d.set_3d_properties(z_all[:idx])\n",
" line_shadow.set_data(x_all[:idx], y_all[:idx])\n",
" line_shadow.set_3d_properties(z_shadow[:idx])\n",
" \n",
" scatter_3d._offsets3d = ([x_all[idx]], [y_all[idx]], [z_all[idx]])\n",
" scatter_shadow._offsets3d = ([x_all[idx]], [y_all[idx]], [0.1])\n",
" scatter_pot.set_offsets(np.c_[Loes[idx, 1], VeffRezl(Loes[0, 1])])\n",
" return fig,\n",
"\n",
"ani = animation.FuncAnimation(\n",
" fig, animate, init_func=init, frames=anzframes, \n",
" interval=100, blit=True\n",
")\n",
"\n",
"plt.close(fig)\n",
"HTML(ani.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Im Folgenden werden die unterschiedlichen Bahnbewegungen um ein schwarzes Loch klassifiziert. Die einzelnen Bewegungstypen lassen sich physikalisch über die Energie $e$ und den Drehimpuls $l$ des Testteilchens relativ zum effektiven Potenzial $V(r,M,l)$ wie folgt charakterisieren: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A) Kreisförmige Bahnen: \n",
"Diese Bahnen existieren an den Extrempunkten des effektiven Potenzials. Man unterscheidet hierbei zwischen stabilen kreisförmigen Bahnen (im Minimum des Potenzials, oberhalb des sogenannten ISCO – Innermost Stable Circular Orbit) und instabilen kreisförmigen Bahnen (auf dem Maximum des Potenzials)."
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"t0 = 0\n",
"phi0 = 0\n",
"dr0 = 0\n",
"setl = 4.1\n",
"setVeffRez = VeffRez.subs({(l,setl),(M,set_M)})\n",
"EqCircOrb = Eq(diff(setVeffRez,r),0)\n",
"r0A = float(solve(EqCircOrb)[1])\n",
"dphi0A = setl/r0A**2\n",
"dt0A = float(LoesEq_ds[0].subs({(r,r0A),(dr,dr0),(dphi,dphi0A),(M,set_M)}))\n",
"setEA = dt0A*((1-2*set_M/r0A))\n",
"initialvalA = np.array([t0,r0A,phi0,dt0A,dr0,dphi0A])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"B) Elliptische Bahnen / Rosettenbahnen: \n",
"Wenn die Energie des Probekörpers größer als das Minimum, aber kleiner als das Maximum des Potenzials ist, resultiert eine gebundene Bewegung. Aufgrund der relativistischen Effekte schließt sich diese Bahn jedoch nicht wie bei Newton (Kepler-Ellipse), sondern führt zu einer markanten Periheldrehung (Einstein-Präzession), wodurch die typische Rosettenform entsteht."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"r0B = 8\n",
"dphi0B = setl/r0B**2\n",
"dt0B = float(LoesEq_ds[0].subs({(r,r0B),(dr,dr0),(dphi,dphi0B),(M,set_M)}))\n",
"setEB = dt0B*(1-2*set_M/r0B)\n",
"initialvalB = np.array([t0,r0B,phi0,dt0B,dr0,dphi0B])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"C) Ungebunden parabolische Bahnen: \n",
"Diese stellen den Grenzfall dar, bei dem der Probekörper exakt die Fluchtenergie besitzt: $e = \\lim\\limits_{r \\to \\infty}V(r,M,l) = 1$ . Das Teilchen kommt theoretisch aus dem Unendlichen mit der Geschwindigkeit Null an, wird vom Schwarzen Loch abgelenkt und entweicht wieder ins Unendliche."
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [],
"source": [
"setEC = float(limit_seq(setVeffRez, r))\n",
"EqE1 = Eq(setVeffRez,setEC)\n",
"r0C = float(solve(EqE1,r)[1])\n",
"dphi0C = setl/r0C**2\n",
"dt0C = float(LoesEq_ds[0].subs({(r,r0C),(dr,dr0),(dphi,dphi0C),(M,set_M)}))\n",
"initialvalC = np.array([t0,r0C,phi0,dt0C,dr0,dphi0C])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"D) Ungebunden hyperbolische Bahnen:\n",
"Hier besitzt das Teilchen eine Überschussenergie: $e > \\lim\\limits_{r \\to \\infty}V(r,M,l) = 1$. Es nähert sich mit einer hohen Anfangsgeschwindigkeit aus dem Unendlichen, erfährt in der Nähe des Ereignishorizonts eine starke gravitative Streuung (oft mit extremen relativistischen Ablenkungswinkeln) und verlässt das System wieder."
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [],
"source": [
"setED = 1.005\n",
"EqE1005 = Eq(setVeffRez,setED)\n",
"r0D = nsolve(EqE1005,4.0)\n",
"r0D = float(re(r0D))\n",
"dphi0D = setl/r0D**2\n",
"dt0D = float(LoesEq_ds[0].subs({(r,r0D),(dr,dr0),(dphi,dphi0D),(M,set_M)}))\n",
"initialvalD = np.array([t0,r0D,phi0,dt0D,dr0,dphi0D])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"E) Einfangbahnen / Capture Orbits:\n",
"Wenn die Energie oder der Drehimpuls des Teilchens so beschaffen sind, dass es die Potenzialbarriere des Schwarzen Lochs überwindet (Energie $e$ ist größer als das Maximum des Potenzials), gibt es keinen klassischen Umkehrpunkt mehr. Das Teilchen spiralisiert unaufhaltsam über den Ereignishorizont hinaus und wird vom Schwarzen Loch dauerhaft verschluckt."
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [],
"source": [
"r0E = 225\n",
"dphi0E = setl/r0E**2\n",
"dr0E=-0.185388257\n",
"dt0E = float(LoesEq_ds[0].subs({(r,r0E),(dr,dr0E),(dphi,dphi0E),(M,set_M)}))\n",
"setEE = dt0E*((1-2*set_M/r0E))\n",
"initialvalE = np.array([t0,r0E,phi0,dt0E,dr0E,dphi0E])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Wir simulieren alle fünf Bahnbewegungen."
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [],
"source": [
"N = 50000\n",
"tauval = np.linspace(0, 1068, N+1)\n",
"LoesA = integrate.odeint(DGLsys, initialvalA, tauval)\n",
"LoesB = integrate.odeint(DGLsys, initialvalB, tauval)\n",
"LoesC = integrate.odeint(DGLsys, initialvalC, tauval)\n",
"LoesD = integrate.odeint(DGLsys, initialvalD, tauval)\n",
"LoesE = integrate.odeint(DGLsys, initialvalE, tauval)\n",
"Loes_vec = [LoesA,LoesB,LoesC,LoesD,LoesE]"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [],
"source": [
"zBett = sqrt(8*M*(r-2*M))\n",
"R = np.linspace(2.00001, 40, 1000)\n",
"PHI = np.linspace(0, 2*np.pi, 300)\n",
"R, PHI = np.meshgrid(R, PHI)\n",
"X = R*np.cos(PHI)\n",
"Y = R*np.sin(PHI)\n",
"zlam = lambdify((x,y), zBett.subs({(M,1),(r,sqrt(x**2+y**2))}))\n",
"ZF = np.array(list(np.real(zlam(X,Y))))\n",
"rval = np.linspace(2.85,40, 1001)"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"anzframes = 100\n",
"step = int(N/anzframes-1) \n",
"xylim = 35\n",
"zlim = 20\n",
"fig = plt.figure(figsize=(11,5))\n",
"gs = gridspec.GridSpec(1, 2, width_ratios=[2,1], wspace=0.21)\n",
"ax1 = plt.subplot(gs[0],projection='3d')\n",
"ax2 = plt.subplot(gs[1])\n",
"ax1.xaxis.pane.fill = False\n",
"ax1.yaxis.pane.fill = False\n",
"ax1.zaxis.pane.fill = False\n",
"ax1.xaxis.pane.set_edgecolor('white')\n",
"ax1.yaxis.pane.set_edgecolor('white')\n",
"ax1.zaxis.pane.set_edgecolor('white')\n",
"\n",
"def init():\n",
" ax1.plot_surface(X, Y, ZF, cmap=cm.nipy_spectral, linewidth=0, alpha=0.5) \n",
" ax1.contourf(X, Y, ZF,100, zdir='z', offset=0, cmap=cm.nipy_spectral,alpha=0.5)\n",
" ax1.scatter(LoesA[0, 1]*np.cos(LoesA[0, 2]),LoesA[0, 1]*np.sin(LoesA[0, 2]),np.real(zlam(LoesA[0, 1]*np.cos(LoesA[0, 2]),LoesA[0, 1]*np.sin(LoesA[0, 2]))),c=\"blue\", s=60, marker='o');\n",
" ax1.scatter(LoesA[0, 1]*np.cos(LoesA[0, 2]),LoesA[0, 1]*np.sin(LoesA[0, 2]),0.1,c=\"blue\", s=40, marker='o');\n",
" ax1.scatter(LoesB[0, 1]*np.cos(LoesB[0, 2]),LoesB[0, 1]*np.sin(LoesB[0, 2]),np.real(zlam(LoesB[0, 1]*np.cos(LoesB[0, 2]),LoesB[0, 1]*np.sin(LoesB[0, 2]))),c=\"red\", s=60, marker='o');\n",
" ax1.scatter(LoesB[0, 1]*np.cos(LoesB[0, 2]),LoesB[0, 1]*np.sin(LoesB[0, 2]),0.1,c=\"red\", s=40, marker='o');\n",
" ax1.scatter(LoesC[0, 1]*np.cos(LoesC[0, 2]),LoesC[0, 1]*np.sin(LoesC[0, 2]),np.real(zlam(LoesC[0, 1]*np.cos(LoesC[0, 2]),LoesC[0, 1]*np.sin(LoesC[0, 2]))),c=\"green\", s=60, marker='o');\n",
" ax1.scatter(LoesC[0, 1]*np.cos(LoesC[0, 2]),LoesC[0, 1]*np.sin(LoesC[0, 2]),0.1,c=\"green\", s=40, marker='o');\n",
" ax1.scatter(LoesD[0, 1]*np.cos(LoesD[0, 2]),LoesD[0, 1]*np.sin(LoesD[0, 2]),np.real(zlam(LoesD[0, 1]*np.cos(LoesD[0, 2]),LoesD[0, 1]*np.sin(LoesD[0, 2]))),c=\"grey\", s=60, marker='o');\n",
" ax1.scatter(LoesD[0, 1]*np.cos(LoesD[0, 2]),LoesD[0, 1]*np.sin(LoesD[0, 2]),0.1,c=\"grey\", s=40, marker='o');\n",
" ax1.scatter(LoesE[0, 1]*np.cos(LoesE[0, 2]),LoesE[0, 1]*np.sin(LoesE[0, 2]),np.real(zlam(LoesE[0, 1]*np.cos(LoesE[0, 2]),LoesE[0, 1]*np.sin(LoesE[0, 2]))),c=\"black\", s=60, marker='o');\n",
" ax1.scatter(LoesE[0, 1]*np.cos(LoesE[0, 2]),LoesE[0, 1]*np.sin(LoesE[0, 2]),0.1,c=\"black\", s=40, marker='o');\n",
" ax2.plot(rval,VeffRezl(rval),c=\"black\", linewidth=1.5, linestyle='-');\n",
" ax2.scatter(r0,VeffRezl(r0),c=\"black\", s=80, marker='o');\n",
" ax1.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
" ax1.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
" ax1.set_zlabel(\"Visualisierung z\");\n",
" ax2.set_ylabel(r\"$\\rm V(r)$\")\n",
" ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
" ax1.view_init(azim=-130, elev=35)\n",
" ax1.set_xlim(-xylim, xylim)\n",
" ax1.set_ylim(-xylim, xylim)\n",
" ax1.set_zlim(0, zlim)\n",
" ax2.set_xlim(2, xylim)\n",
" ax1.grid(False)\n",
" return fig,\n",
"\n",
"def animate(i):\n",
" ax1.cla() \n",
" ax2.cla()\n",
" ax1.plot_surface(X, Y, ZF, cmap=cm.nipy_spectral, linewidth=0, alpha=0.5)\n",
" ax1.contourf(X, Y, ZF,100, zdir='z', offset=0, cmap=cm.nipy_spectral,alpha=0.5)\n",
" Loes = LoesA\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),np.real(zlam(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]))),c=\"blue\", linewidth=1, linestyle='-');\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),0.1,c=\"blue\", linewidth=2.5, linestyle='-');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),np.real(zlam(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]))),c=\"blue\", s=60, marker='o');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),0.1,c=\"blue\", s=40, marker='o');\n",
" Loes = LoesB\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),np.real(zlam(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]))),c=\"red\", linewidth=1, linestyle='-');\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),0.1,c=\"red\", linewidth=2.5, linestyle='-');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),np.real(zlam(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]))),c=\"red\", s=60, marker='o');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),0.1,c=\"red\", s=40, marker='o');\n",
" Loes = LoesC\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),np.real(zlam(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]))),c=\"green\", linewidth=1, linestyle='-');\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),0.1,c=\"green\", linewidth=2.5, linestyle='-');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),np.real(zlam(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]))),c=\"green\", s=60, marker='o');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),0.1,c=\"green\", s=40, marker='o');\n",
" Loes = LoesD\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),np.real(zlam(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]))),c=\"grey\", linewidth=1, linestyle='-');\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),0.1,c=\"grey\", linewidth=2.5, linestyle='-');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),np.real(zlam(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]))),c=\"grey\", s=60, marker='o');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),0.1,c=\"grey\", s=40, marker='o');\n",
" Loes = LoesE\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),np.real(zlam(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]))),c=\"black\", linewidth=1, linestyle='-');\n",
" ax1.plot(Loes[:step*i, 1]*np.cos(Loes[:step*i, 2]),Loes[:step*i, 1]*np.sin(Loes[:step*i, 2]),0.1,c=\"black\", linewidth=2.5, linestyle='-');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),np.real(zlam(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]))),c=\"black\", s=60, marker='o');\n",
" ax1.scatter(Loes[step*i, 1]*np.cos(Loes[step*i, 2]),Loes[step*i, 1]*np.sin(Loes[step*i, 2]),0.1,c=\"black\", s=40, marker='o');\n",
"\n",
" ax2.plot(rval,VeffRezl(rval),c=\"black\", linewidth=1.5, linestyle='-');\n",
" ax2.scatter(LoesA[step*i, 1],VeffRezl(LoesA[0, 1]),c=\"blue\", s=80, marker='o');\n",
" ax2.scatter(LoesB[step*i, 1],VeffRezl(LoesB[0, 1]),c=\"red\", s=80, marker='o');\n",
" ax2.plot(LoesB[:step*i, 1],VeffRezl(LoesB[0, 1]*LoesB[:step*i, 1]/LoesB[:step*i, 1]),c=\"red\", linewidth=1, linestyle=':');\n",
" ax2.scatter(LoesC[step*i, 1],VeffRezl(LoesC[0, 1]),c=\"green\", s=80, marker='o');\n",
" ax2.plot(LoesC[:step*i, 1],VeffRezl(LoesC[0, 1]*LoesC[:step*i, 1]/LoesC[:step*i, 1]),c=\"green\", linewidth=1, linestyle=':');\n",
" ax2.scatter(LoesD[step*i, 1],VeffRezl(LoesD[0, 1]),c=\"grey\", s=80, marker='o');\n",
" ax2.plot(LoesD[:step*i, 1],VeffRezl(LoesD[0, 1]*LoesD[:step*i, 1]/LoesD[:step*i, 1]),c=\"grey\", linewidth=1, linestyle=':');\n",
" ax2.scatter(LoesE[step*i, 1],setEE,c=\"black\", s=80, marker='o');\n",
" ax2.plot(LoesE[:step*i, 1],setEE*LoesE[:step*i, 1]/LoesE[:step*i, 1],c=\"black\", linewidth=1, linestyle=':');\n",
" \n",
" \n",
" ax1.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
" ax1.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
" ax1.set_zlabel(\"Einbettung z\");\n",
" ax2.set_ylabel(r\"$\\rm V(r)$\")\n",
" ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
" ax1.view_init(azim=-130, elev=35)\n",
" ax1.set_xlim(-xylim, xylim)\n",
" ax1.set_ylim(-xylim, xylim)\n",
" ax1.set_zlim(0, zlim) \n",
" ax2.set_xlim(2, xylim)\n",
" ax1.grid(False)\n",
" return fig,\n",
"\n",
"ani = animation.FuncAnimation(fig,animate,init_func=init,frames=anzframes,interval=100)\n",
"plt.close(ani._fig)\n",
"HTML(ani.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"bzw. ohne Verwendung von ax1.cla() und ax2.cla() in jedem Animationsschritt und mit einer Trennung von Animationsobjekten und statischen Elementen."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"anzframes = 100\n",
"step = int(N/anzframes-1) \n",
"xylim = 35\n",
"zlim = 20\n",
"\n",
"# Figure-Setup\n",
"fig = plt.figure(figsize=(11, 5))\n",
"gs = gridspec.GridSpec(1, 2, width_ratios=[2, 1], wspace=0.21)\n",
"ax1 = plt.subplot(gs[0], projection='3d')\n",
"ax2 = plt.subplot(gs[1])\n",
"\n",
"for axis in [ax1.xaxis, ax1.yaxis, ax1.zaxis]:\n",
" axis.pane.fill = False\n",
" axis.pane.set_edgecolor('white')\n",
"\n",
"ax1.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
"ax1.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
"ax1.set_zlabel(\"Einbettung z\")\n",
"ax1.set_xlim(-xylim, xylim)\n",
"ax1.set_ylim(-xylim, xylim)\n",
"ax1.set_zlim(0, zlim)\n",
"ax1.view_init(azim=-130, elev=35)\n",
"ax1.grid(False)\n",
"\n",
"v_values = VeffRezl(rval)\n",
"ax2.set_ylabel(r\"$\\rm V(r)$\")\n",
"ax2.set_xlabel(r\"$\\rm Radius \\, r \\,[km]$\")\n",
"ax2.set_xlim(np.min(rval), np.max(rval))\n",
"\n",
"# Statische Hintergründe zeichnen\n",
"ax1.plot_surface(X, Y, ZF, cmap=cm.nipy_spectral, linewidth=0, alpha=0.5)\n",
"ax1.contourf(X, Y, ZF, 100, zdir='z', offset=0, cmap=cm.nipy_spectral, alpha=0.5)\n",
"ax2.plot(rval, v_values, c=\"black\", linewidth=1.5, linestyle='-')\n",
"\n",
"# Animationsobjekte\n",
"lines_3d = []\n",
"lines_shadow = []\n",
"scatters_3d = []\n",
"scatters_shadow = []\n",
"scatters_pot = []\n",
"lines_pot = []\n",
"\n",
"colors = [\"blue\", \"red\", \"green\", \"gray\", \"black\"]\n",
"for c in colors:\n",
" l3d, = ax1.plot([], [], [], c=c, linewidth=1.2, linestyle='-')\n",
" lsh, = ax1.plot([], [], [], c=c, linewidth=2.0, linestyle='-', alpha=0.6)\n",
" lines_3d.append(l3d)\n",
" lines_shadow.append(lsh)\n",
" scatters_3d.append(ax1.scatter([], [], [], c=c, s=50, marker='o'))\n",
" scatters_shadow.append(ax1.scatter([], [], [], c=c, s=30, marker='o'))\n",
" scatters_pot.append(ax2.scatter([], [], c=c, s=60, marker='o', zorder=5))\n",
" lpot, = ax2.plot([], [], c=c, linewidth=1, linestyle=':', alpha=0.7)\n",
" lines_pot.append(lpot)\n",
"\n",
"x_all_vec = []\n",
"y_all_vec = []\n",
"z_all_vec = []\n",
"for Loes in Loes_vec:\n",
" x_all = Loes[:, 1] * np.cos(Loes[:, 2])\n",
" y_all = Loes[:, 1] * np.sin(Loes[:, 2])\n",
" z_all = np.real(zlam(x_all, y_all)) \n",
" x_all_vec.append(x_all)\n",
" y_all_vec.append(y_all)\n",
" z_all_vec.append(z_all)\n",
"\n",
"def init():\n",
" for j in range(5):\n",
" lines_3d[j].set_data([], [])\n",
" lines_3d[j].set_3d_properties([])\n",
" lines_shadow[j].set_data([], [])\n",
" lines_shadow[j].set_3d_properties([]) \n",
" scatters_3d[j]._offsets3d = ([], [], [])\n",
" scatters_shadow[j]._offsets3d = ([], [], [])\n",
" scatters_pot[j].set_offsets(np.empty((0, 2)))\n",
" lines_pot[j].set_data([], [])\n",
" return fig,\n",
"\n",
"def animate(i):\n",
" idx = step * i\n",
" for j in range(5):\n",
" Loes = Loes_vec[j]\n",
" x_all = x_all_vec[j]\n",
" y_all = y_all_vec[j]\n",
" z_all = z_all_vec[j]\n",
" \n",
" lines_3d[j].set_data(x_all[:idx], y_all[:idx])\n",
" lines_3d[j].set_3d_properties(z_all[:idx])\n",
" lines_shadow[j].set_data(x_all[:idx], y_all[:idx])\n",
" lines_shadow[j].set_3d_properties(np.full_like(x_all[:idx], 0.1))\n",
" scatters_3d[j]._offsets3d = ([x_all[idx]], [y_all[idx]], [z_all[idx]])\n",
" scatters_shadow[j]._offsets3d = ([x_all[idx]], [y_all[idx]], [0.1])\n",
" \n",
" r_hist = Loes[:idx, 1]\n",
" if(j < 4):\n",
" v_hist = VeffRezl(Loes[0, 1])\n",
" else:\n",
" v_hist = setEE \n",
" if(len(r_hist) > 0):\n",
" scatters_pot[j].set_offsets(np.c_[r_hist[-1], v_hist])\n",
" lines_pot[j].set_data(r_hist, [v_hist]*len(r_hist)) \n",
" return fig,\n",
"\n",
"ani = animation.FuncAnimation(\n",
" fig, animate, init_func=init, frames=anzframes, \n",
" interval=100, blit=True\n",
")\n",
"\n",
"plt.close(fig)\n",
"HTML(ani.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In der oberen Animation erkennt man neben den gebundenen kreisförmigen (A: blau) und elliptischen (B: rot) Bahnen, den parabolischen (C: grün) und hyperbolischen (D: grau) Bahnverläufen auch eine durch das schwarze Loch eingefangene Bahn (E: capture orbit, schwarz). Diese ist in der unteren Abbildung nochmals separat veranschaulicht."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Loes = LoesE\n",
"ax = plt.gca()\n",
"ax.cla() \n",
"ax.set_ylabel(r\"$\\rm y \\,[km]$\")\n",
"ax.set_xlabel(r\"$\\rm x \\,[km]$\")\n",
"ax.plot(Loes[:, 1]*np.cos(Loes[:, 2]),Loes[:, 1]*np.sin(Loes[:, 2]),c=\"black\", linewidth=1.5, linestyle='-');\n",
"ax.scatter(Loes[0, 1]*np.cos(Loes[0, 2]),Loes[0, 1]*np.sin(Loes[0, 2]),c=\"black\", s=60, marker='o');\n",
"ax.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Die Visualisierung kann man auch mittels der \"Plotly Python Open Source Graphing Library\" erstellen ( siehe https://plotly.com/python/ ). In der folgenden interaktiven Abbildung wird der \"Capture orbit\" und der \"Elliptische Orbit\" visualisiert. Zusätzlich wird die Eigen- und Koordinatenzeit ausgegeben, wenn man mit der Maus genau auf eine der beiden Probekörper-Trajektorien fokussiert. "
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [],
"source": [
"import plotly.graph_objects as go"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"trichter = go.Surface(x=X, y=Y, z=ZF, colorscale=\"spectral_r\", showscale=True, name=\"Embedded Surface\", hoverinfo='none')\n",
"\n",
"Loes = LoesE\n",
"labels = []\n",
"for i in range(len(Loes[:, 0])):\n",
" labels.append('Eigenzeit '+str(round(tauval[i], 2))+', Koordinatenzeit = '+str(round(Loes[i, 0], 2)))\n",
"capture_orbit =go.Scatter3d(\n",
" x = Loes[:, 1]*np.cos(Loes[:, 2]),\n",
" y = Loes[:, 1]*np.sin(Loes[:, 2]),\n",
" z = np.real(zlam(Loes[:, 1]*np.cos(Loes[:, 2]),Loes[:, 1]*np.sin(Loes[:, 2]))),\n",
" name = \"Capture Orbit\",\n",
" mode = 'lines',\n",
" line = dict(color='black', width=8),\n",
" text = labels,\n",
" hoverinfo = 'text'\n",
" )\n",
"\n",
"Loes = LoesB\n",
"labels = []\n",
"for i in range(len(Loes[:, 0])):\n",
" labels.append('Eigenzeit '+str(round(tauval[i], 2))+', Koordinatenzeit = '+str(round(Loes[i, 0], 2)))\n",
"elliptic_orbit =go.Scatter3d(\n",
" x = Loes[:, 1]*np.cos(Loes[:, 2]),\n",
" y = Loes[:, 1]*np.sin(Loes[:, 2]),\n",
" z = np.real(zlam(Loes[:, 1]*np.cos(Loes[:, 2]),Loes[:, 1]*np.sin(Loes[:, 2]))),\n",
" name = \"Elliptische Bahn\",\n",
" mode = 'lines',\n",
" line = dict(color='red', width=8),\n",
" text = labels,\n",
" hoverinfo = 'text'\n",
" )\n",
"\n",
"layout = go.Layout(autosize=True,\n",
" width=700, height=700,\n",
" margin=dict(l=15, r=50, b=65, t=90),\n",
" scene_aspectmode='cube',\n",
" scene = dict(\n",
" xaxis_showbackground = False,\n",
" yaxis_showbackground = False,\n",
" zaxis_showbackground = False,\n",
" xaxis_gridcolor = \"lightgrey\",\n",
" yaxis_gridcolor = \"lightgrey\",\n",
" zaxis_gridcolor = \"lightgrey\",\n",
" xaxis_range = [-40,40],\n",
" yaxis_range = [-40,40],\n",
" zaxis_range = [0,20],\n",
" xaxis_title = 'x',\n",
" yaxis_title = 'y',\n",
" zaxis_title = 'f'),\n",
" legend=dict(\n",
" yanchor = \"top\",\n",
" y=0.99,\n",
" xanchor = \"left\",\n",
" x=0.01)\n",
" )\n",
"\n",
"data = [trichter,elliptic_orbit,capture_orbit]\n",
"fig = go.Figure(data = data, layout = layout)\n",
"\n",
"fig.show(renderer='iframe')"
]
}
],
"metadata": {
"kernelspec": {
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