{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Plots of geodesics in Kerr spacetime\n", "## Computation with `kerrgeodesic_gw`\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://relativite.obspm.fr/blackholes/).\n", "\n", "It requires [SageMath](http://www.sagemath.org/) (version $\\geq$ 8.2), with the package [kerrgeodesic_gw](https://github.com/BlackHolePerturbationToolkit/kerrgeodesic_gw) (version $\\geq$ 0.3). To install the latter, simply run \n", "```\n", "sage -pip install kerrgeodesic_gw\n", "```\n", "in a terminal." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.2, Release Date: 2020-10-24'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we set up the notebook to use LaTeX-formatted display:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and we ask for CPU demanding computations to be performed in parallel on 8 processes:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "Parallelism().set(nproc=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A Kerr black bole is entirely defined by two parameters $(m, a)$, where $m$ is the black hole mass and $a$ is the black hole angular momentum divided by $m$.\n", "In this notebook, we shall set $m=1$ and we denote the angular momentum parameter $a$ by the symbolic variable `a`, using `a0` for a specific numerical value:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "a = var('a')\n", "a0 = 0.998" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The spacetime object is created as an instance of the class `KerrBH`:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Kerr spacetime M\n" ] } ], "source": [ "from kerrgeodesic_gw import KerrBH\n", "M = KerrBH(a)\n", "print(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Boyer-Lindquist coordinate $r$ of the event horizon:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sqrt{-a^{2} + 1} + 1\n", "\\end{math}" ], "text/plain": [ "sqrt(-a^2 + 1) + 1" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rH = M.event_horizon_radius()\n", "rH" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.06321392251712\n", "\\end{math}" ], "text/plain": [ "1.06321392251712" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rH0 = rH.subs({a: a0})\n", "rH0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The method `boyer_lindquist_coordinates()` returns the chart of Boyer-Lindquist coordinates `BL` and allows the user to instanciate the Python variables `(t, r, th, ph)` to the coordinates $(t,r,\\theta,\\phi)$:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,(t, r, {\\theta}, {\\phi})\\right)\n", "\\end{math}" ], "text/plain": [ "Chart (M, (t, r, th, ph))" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BL. = M.boyer_lindquist_coordinates()\n", "BL" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The metric tensor is naturally returned by the method `metric()`:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( -\\frac{a^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} - 2 \\, r}{a^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( -\\frac{2 \\, a r \\sin\\left({\\theta}\\right)^{2}}{a^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} {\\phi} + \\left( \\frac{a^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}}{a^{2} + r^{2} - 2 \\, r} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( a^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{2 \\, a r \\sin\\left({\\theta}\\right)^{2}}{a^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, a^{2} r \\sin\\left({\\theta}\\right)^{4} + {\\left(a^{2} r^{2} + r^{4} + {\\left(a^{4} + a^{2} r^{2}\\right)} \\cos\\left({\\theta}\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{a^{2} \\cos\\left({\\theta}\\right)^{2} + r^{2}} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\n", "\\end{math}" ], "text/plain": [ "g = -(a^2*cos(th)^2 + r^2 - 2*r)/(a^2*cos(th)^2 + r^2) dt*dt - 2*a*r*sin(th)^2/(a^2*cos(th)^2 + r^2) dt*dph + (a^2*cos(th)^2 + r^2)/(a^2 + r^2 - 2*r) dr*dr + (a^2*cos(th)^2 + r^2) dth*dth - 2*a*r*sin(th)^2/(a^2*cos(th)^2 + r^2) dph*dt + (2*a^2*r*sin(th)^4 + (a^2*r^2 + r^4 + (a^4 + a^2*r^2)*cos(th)^2)*sin(th)^2)/(a^2*cos(th)^2 + r^2) dph*dph" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = M.metric()\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bound timelike geodesic" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We set $\\mu=1$ and pick some values of $E$, $L$ and $Q$, with $E<1$ to ensure that we are dealing with a bound geodesic:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "mu = 1\n", "E = 0.9\n", "#L = 1.9\n", "L = 2.\n", "Q = 1.3" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "r = var('r')\n", "R(r) = ((E^2 - 1)*r^4 + 2*r^3 + (a0^2*(E^2 - 1) - Q - L^2)*r^2 \n", " + 2*(Q + (L - a0*E)^2)*r - a0^2*Q)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = plot(-R(r), (r, -1.5, 7.5), thickness=1.5,\n", " axes_labels=[r'$r/m$', r'$-\\mathcal{R}(r)/m^4$'])\n", "graph" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2.1752102281015393\n", "\\end{math}" ], "text/plain": [ "2.1752102281015393" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rp = find_root(R(r), 1.5, 4)\n", "rp" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}6.852695179907905\n", "\\end{math}" ], "text/plain": [ "6.852695179907905" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ra = find_root(R(r), 5, 10)\n", "ra" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph += line([(rp, 0), (ra, 0)], thickness=2.5, color='red') \\\n", " + text(r'$r_{\\rm p}$', (1.05*rp, -2.5), color='red', fontsize=16) \\\n", " + text(r'$r_{\\rm a}$', (1.02*ra, -2.5), color='red', fontsize=16) \n", "graph += line([(rH0, -20), (rH0, 30)], thickness=2, color='black')\n", "graph" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zoom = plot(-R(r), (r, -0.1, 2.5), thickness=1.5, \n", " axes_labels=[r'$r/m$', r'$-\\mathcal{R}(r)/m^4$'])\n", "zoom += line([(rp, 0), (2.5, 0)], thickness=2.5, color='red') \\\n", " + text(r'$r_{\\rm p}$', (1.01*rp, 0.2), color='red', fontsize=12)\n", "zoom += line([(rH0, -0.8), (rH0, 1.8)], thickness=2, color='black')\n", "zoom" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Multigraphics with 2 elements" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = graph.inset(zoom, (0.7, 0.7, 0.3, 0.3), fontsize=8)\n", "graph" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "graph.save(\"gek_R_potential.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us choose the initial point $P$ for the geodesic:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point P on the Kerr spacetime M\n" ] } ], "source": [ "P = M.point((0, (rp + ra)/2, pi/2, 0), name='P')\n", "print(P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A geodesic is constructed by providing the range $[\\lambda_{\\rm min},\\lambda_{\\rm max}]$ of the affine parameter $\\lambda$, the initial point and either \n", " - (i) the Boyer-Lindquist components $(p^t_0, p^r_0, p^\\theta_0, p^\\phi_0)$ of the initial 4-momentum vector\n", " $p_0 = \\left. \\frac{\\mathrm{d}x}{\\mathrm{d}\\lambda}\\right| _{\\lambda_{\\rm min}}$,\n", " - (ii) the four integral of motions $(\\mu, E, L, Q)$\n", " - or (iii) some of the components of $p_0$ along with with some integrals of motion. \n", "We shall also specify some numerical value for the Kerr spin parameter $a$.\n", "\n", "Here, we choose $\\lambda\\in[0, 600\\, m]$, the option (ii) and \n", "$a=0.998 \\,m$, where $m$ in the black hole mass::\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "lmax = 600 # lambda_max" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initial tangent vector: \n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}p = 1.51876198038160 \\frac{\\partial}{\\partial t } + 0.187663512911857 \\frac{\\partial}{\\partial r } + 0.0559574180643787 \\frac{\\partial}{\\partial {\\theta} } + 0.122475774691562 \\frac{\\partial}{\\partial {\\phi} }\n", "\\end{math}" ], "text/plain": [ "p = 1.51876198038160 d/dt + 0.187663512911857 d/dr + 0.0559574180643787 d/dth + 0.122475774691562 d/dph" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "The curve was correctly set.\n", "Parameters appearing in the differential system defining the curve are [a].\n" ] } ], "source": [ "Li = M.geodesic([0, lmax], P, mu=mu, E=E, L=L, Q=Q, a_num=0.998,\n", " name='Li', latex_name=r'\\mathcal{L}', verbose=True)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Geodesic Li of the Kerr spacetime M\n" ] } ], "source": [ "print(Li)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The numerical integration of the geodesic equation is performed via `integrate()`, by providing the integration step $\\delta\\lambda$ in units of $m$:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "Li.integrate(step=0.005)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then plot the geodesic:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Li.plot(plot_points=2000, thickness=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Actually, many options can be passed to the method `plot()`. For instance to a get a 3D spacetime diagram:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Li.plot(coordinates='txy', thickness=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or to get the trace of the geodesic in the $(x,y)$ plane:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = Li.plot(coordinates='xy', plot_points=2000, thickness=1.5, \n", " axes_labels=[r'$x/m$', r'$y/m$'])\n", "graph" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "graph.save(\"gek_timelike_xy.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or else to get the trace in the $(x,z)$ plane:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = Li.plot(coordinates='xz', plot_points=2000, thickness=1.5, \n", " axes_labels=[r'$x/m$', r'$z/m$'])\n", "graph" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "graph.save(\"gek_timelike_xz.pdf\")" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(\\frac{4.00000000000000}{\\sin\\left({\\theta}\\right)^{2}} + 0.189240760000000\\right)} \\cos\\left({\\theta}\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "(4.00000000000000/sin(th)^2 + 0.189240760000000)*cos(th)^2" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "th = var('th', latex_name=r'\\theta')\n", "V(th) = cos(th)^2 * (a0^2*(1 - E^2) + L^2/sin(th)^2)\n", "V(th)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = plot(V(th), (th, 0.7, pi-0.7), axes_labels=[r'$\\theta$', r'$V(\\theta)$'])\n", "graph += line([(0, Q), (pi, Q)], color='red')\n", "graph" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.060238228434118\n", "\\end{math}" ], "text/plain": [ "1.060238228434118" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "th_min = find_root(V(th) - Q, 0.5, pi/2)\n", "th_min" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Analytic formula for $\\theta_{\\rm min}$:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.06023822843412\n", "\\end{math}" ], "text/plain": [ "1.06023822843412" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A2 = a0^2*(mu^2 - E^2)\n", "sthm = (A2 - L^2 - Q + sqrt((L^2 + Q - A2)^2 + 4*L^2*A2))/(2*A2)\n", "th_min0 = arcsin(sqrt(sthm))\n", "th_min0" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-8.88178419700125 \\times 10^{-16}\n", "\\end{math}" ], "text/plain": [ "-8.88178419700125e-16" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "th_min - th_min0" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}60.7471757677022\n", "\\end{math}" ], "text/plain": [ "60.7471757677022" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "th_min_deg = n(th_min/pi*180)\n", "th_min_deg" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}29.2528242322978\n", "\\end{math}" ], "text/plain": [ "29.2528242322978" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "th_inc_deg = 90 - th_min_deg\n", "th_inc_deg" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}3.3022172855673317\n", "\\end{math}" ], "text/plain": [ "3.3022172855673317" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p_K = 2*ra*rp/(ra + rp)\n", "p_K" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.5181140852070248\n", "\\end{math}" ], "text/plain": [ "0.5181140852070248" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e_K = (ra - rp)/(ra + rp)\n", "e_K" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that the values of $\\mu$, $E$, $L$ and $Q$ evaluated at $\\lambda=300 \\, m$ are equal to those at $\\lambda=0$ up to the numerical accuracy of the integration scheme:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
quantityvalueinitial valuediff.relative diff.
\n", "
" ], "text/plain": [ " quantity value initial value diff. relative diff.\n", " $\\mu$ 0.9999976785567484 1.0 -2.321e-6 -2.321e-6\n", " $E$ 0.899985179453538 0.900000000000000 -0.00001482 -0.00001647\n", " $L$ 1.99982956873133 2.00000000000000 -0.0001704 -0.00008522\n", " $Q$ 1.29980808952398 1.30000000000000 -0.0001919 -0.0001476" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Li.check_integrals_of_motion(lmax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Decreasing the integration step leads to smaller errors:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
quantityvalueinitial valuediff.relative diff.
\n", "
" ], "text/plain": [ " quantity value initial value diff. relative diff.\n", " $\\mu$ 0.999999536576446 1.0 -4.634e-7 -4.634e-7\n", " $E$ 0.899997039643679 0.900000000000000 -2.960e-6 -3.289e-6\n", " $L$ 1.99996601125880 2.00000000000000 -0.00003399 -0.00001699\n", " $Q$ 1.29996145780904 1.30000000000000 -0.00003854 -0.00002965" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Li.integrate(step=0.001)\n", "Li.check_integrals_of_motion(lmax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ingoing null geodesic with negative angular momentum" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We choose a ingoing null geodesic in the equatorial plane with $L = -6 E < 0$, starting at the point of Boyer-Lindquist coordinates $(t,r,\\theta,\\phi) = (0, 12, \\pi/2, 0)$:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initial tangent vector: \n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}p = 1.20797381595070 \\frac{\\partial}{\\partial t } -0.901996260873419 \\frac{\\partial}{\\partial r } -0.0399489777089388 \\frac{\\partial}{\\partial {\\phi} }\n", "\\end{math}" ], "text/plain": [ "p = 1.20797381595070 d/dt - 0.901996260873419 d/dr - 0.0399489777089388 d/dph" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "The curve was correctly set.\n", "Parameters appearing in the differential system defining the curve are [a].\n" ] } ], "source": [ "lmax = 13.07\n", "Li = M.geodesic([0, lmax], M((0,12,pi/2,0)), mu=0, E=1, L=-6, Q=0,\n", " r_increase=False, a_num=a0, \n", " name='Li', latex_name=r'\\mathcal{L}', verbose=True)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "Li.integrate(step=0.00002)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = Li.plot(coordinates='xy', color='green', prange=[0, lmax], plot_points=40000, \n", " thickness=1.5, display_tangent=True, scale=0.0001, \n", " color_tangent='green', plot_points_tangent=4, \n", " axes_labels=[r'$x/m$', r'$y/m$'])\n", "graph" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "graph.save('gek_winding_null.pdf')" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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quantityvalueinitial valuediff.relative diff.
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" ], "text/plain": [ " quantity value initial value diff. relative diff.\n", " $\\mu$ 0.00444310201139289 5.47028152480290e-9 0.004443 812200.\n", " $E$ 1.00000024333053 1.00000000000000 2.433e-7 2.433e-7\n", " $L$ -5.99999942161639 -6.00000000000000 5.784e-7 -9.640e-8\n", " $Q$ 1.31244009464357e-31 0 1.312e-31 -" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Li.check_integrals_of_motion(0.9999*lmax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ingoing time geodesic with zero angular momentum" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initial tangent vector: \n" ] }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}p = 1.15374191268376 \\frac{\\partial}{\\partial t } -0.365955677542959 \\frac{\\partial}{\\partial r } + 0.000678925406390768 \\frac{\\partial}{\\partial {\\phi} }\n", "\\end{math}" ], "text/plain": [ "p = 1.15374191268376 d/dt - 0.365955677542959 d/dr + 0.000678925406390768 d/dph" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "The curve was correctly set.\n", "Parameters appearing in the differential system defining the curve are [a].\n" ] } ], "source": [ "lmax = 26.41\n", "Li = M.geodesic([0, lmax], M((0,15,pi/2,0)), mu=1, E=1, L=0, Q=0,\n", " r_increase=False, a_num=a0, \n", " name='Li', latex_name=r'\\mathcal{L}', verbose=True)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "Li.integrate(step=0.0002)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 8 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = Li.plot(coordinates='xy', color='red', prange=[0, lmax], plot_points=40000, \n", " thickness=1.5, display_tangent=True, scale=0.0001, \n", " color_tangent='red', plot_points_tangent=6, \n", " axes_labels=[r'$x/m$', r'$y/m$'])\n", "show(graph, ymin=-2, ymax=3)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "graph.save('gek_frame_dragging.pdf')" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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quantityvalueinitial valuediff.relative diff.
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" ], "text/plain": [ " quantity value initial value diff. relative diff.\n", " $\\mu$ 1.00001380801330 1.00000000000000 0.00001381 0.00001381\n", " $E$ 1.00000064318726 1.00000000000000 6.432e-7 6.432e-7\n", " $L$ 1.45776391491381e-6 2.77555756156289e-17 1.458e-6 5.252e10\n", " $Q$ 9.83266149777550e-38 0 9.833e-38 -" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Li.check_integrals_of_motion(0.9999*lmax)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.2", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 2 }