{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Zero-energy null geodesics in Kerr spacetime\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://luth.obspm.fr/~luthier/gourgoulhon/bh16/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.2.rc3, Release Date: 2020-10-18'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "a = 0.9" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}L \\ {\\mapsto}\\ -\\sqrt{-\\frac{0.810000000000000}{L^{2} + 1} + 1} + 1\n", "\\end{math}" ], "text/plain": [ "L |--> -sqrt(-0.810000000000000/(L^2 + 1) + 1) + 1" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_min(L) = 1 - sqrt(1 - a^2/(1 + L^2))\n", "r_min" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}L \\ {\\mapsto}\\ \\sqrt{-\\frac{0.810000000000000}{L^{2} + 1} + 1} + 1\n", "\\end{math}" ], "text/plain": [ "L |--> sqrt(-0.810000000000000/(L^2 + 1) + 1) + 1" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_max(L) = 1 + sqrt(1 - a^2/(1 + L^2))\n", "r_max" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "th_min(L) = atan(-L)\n", "th_max(L) = pi - th_min(L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $r$ as a function of $\\theta$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def rf(th, K, L, s):\n", " b = sqrt(1 - a^2/(1 + L^2))\n", " return 1 + b*sin(K - s*arcsin(sqrt(1 + L^2)*cos(th)))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def Kf(rm, L, s):\n", " return n(arcsin((rm - 1)/sqrt(1 - a^2/(1 + L^2))) + s*pi/2)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0.228637568972924, 1.77136243102708\\right)\n", "\\end{math}" ], "text/plain": [ "(0.228637568972924, 1.77136243102708)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L1 = -1\n", "r_min(L1), r_max(L1)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0.785398163397448, 2.35619449019234\\right)\n", "\\end{math}" ], "text/plain": [ "(0.785398163397448, 2.35619449019234)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n(th_min(L1)), n(th_max(L1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot in O'Neill coordinates\n", "$$x = e^{r/m}\\sin\\theta$$\n", "$$y = e^{r/m}\\cos\\theta$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def plot_geod(L1, rm):\n", " K1 = Kf(rm, L1, 1)\n", " K2 = Kf(rm, L1, -1)\n", " xx = lambda th: exp(rf(th, K1, L1, 1))*sin(th)\n", " yy = lambda th: exp(rf(th, K1, L1, 1))*cos(th)\n", " g = parametric_plot((xx, yy), (th_min(L1), th_max(L1)), \n", " thickness=2., color='green')\n", " xx = lambda th: exp(rf(th, K2, L1, -1))*sin(th)\n", " yy = lambda th: exp(rf(th, K2, L1, -1))*cos(th)\n", " g += parametric_plot((xx, yy), (th_min(L1), th_max(L1)), \n", " thickness=2., color='green')\n", " return g" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def plot_arrow(L1, rm, th, dth, s):\n", " K1 = Kf(rm, L1, s)\n", " x1 = n(exp(rf(th, K1, L1, s))*sin(th))\n", " y1 = n(exp(rf(th, K1, L1, s))*cos(th))\n", " th2 = th + dth\n", " x2 = n(exp(rf(th2, K1, L1, s))*sin(th2))\n", " y2 = n(exp(rf(th2, K1, L1, s))*cos(th2))\n", " v = vector([x2 - x1, y2 - y1])\n", " g = v.plot(start=(x1, y1), color='green')\n", " return g" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "g = plot_geod(-1, 1.5)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(1.43588989435407, 0.564110105645933\\right)\n", "\\end{math}" ], "text/plain": [ "(1.43588989435407, 0.564110105645933)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rp = 1 + sqrt(1 - a^2)\n", "rm = 1 - sqrt(1 - a^2)\n", "rp, rm" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta = var('theta')\n", "Rp = exp(rp)\n", "Rm = exp(rm)\n", "Hp = parametric_plot((Rp*sin(theta), Rp*cos(theta)), (theta, 0, pi), color='black', thickness=3) + \\\n", " text(r'$r\\!=\\!r_+$', (2.5, 4.), color='black', fontsize=16)\n", "Hm = parametric_plot((Rm*sin(theta), Rm*cos(theta)), (theta, 0, pi), color='peru', thickness=3) + \\\n", " text(r'$r\\!=\\!r_-$', (1.2, 2.), color='peru', fontsize=16)\n", "R0 = parametric_plot((sin(theta), cos(theta)), (theta, 0, pi), color='darkorange', \n", " linestyle='dotted', thickness=3) + \\\n", " text(r'$r\\!=\\!0$', (0,-1.3), color='darkorange', fontsize=16)\n", "sing = circle((1,0), 0.1, color='red', fill=True) \n", "rminf = circle((0,0), 0.1, edgecolor='black', facecolor='white', fill=True)\n", "g += Hp + Hm + R0 + sing + rminf \n", "g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Arrows:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "g += plot_arrow(-1, 1.5, 1.4, -0.01, 1)\n", "g += plot_arrow(-1, 1.5, 1.1, 0.01, -1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Point $A$:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 14 graphics primitives" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L1 = -1\n", "rm = 1.5\n", "K1 = Kf(rm, L1, 1)\n", "xA = exp(rf(pi/2, K1, L1, 1))\n", "g += circle((xA,0), 0.1, color='green', fill=True)\n", "g += text(r'$A$', (4.7, 0.4), color='green', fontsize=16)\n", "g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot of the ergoregion" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x,y = var('x y')\n", "r = 1/2*ln(x^2 + y^2)\n", "costh2 = y^2/(x^2+y^2)\n", "f_ergo = r^2 - 2*r + a^2*costh2\n", "ergo = region_plot(f_ergo < 0, (x, 0, 8), (y, -5, 5), incol='whitesmoke', \n", " bordercol='grey',\n", " axes_labels=[r'$\\mathrm{e}^{r/m}\\sin\\theta$', \n", " r'$\\mathrm{e}^{r/m}\\cos\\theta$'])\n", "g += ergo\n", "g" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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