{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Meridional plots in Kerr spacetime for $a/m=0.50$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "O'Neill exponential coordinates:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "x,y = var('x y')\n", "r = 1/2*ln(x^2 + y^2)\n", "costh2 = y^2/(x^2+y^2)\n", "sinth2 = x^2/(x^2+y^2)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Function $f$ defining the ergoregion by $f<0$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/4*log(x^2 + y^2)^2 + 0.250000000000000*y^2/(x^2 + y^2) - log(x^2 + y^2)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = 0.5\n", "f = r^2 -2*r + a^2*costh2\n", "f" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "ergo = region_plot(f < 0, (x,-8, 8), (y, -7, 7), incol='lightgray', \n", " bordercol='grey',\n", " axes_labels=[r'$\\mathrm{e}^{r/m}\\sin\\theta$', \n", " r'$\\mathrm{e}^{r/m}\\cos\\theta$'])\n", "ergo += text(r'$\\mathscr{E}^+$', (1.1*e^2, 0.5*e), color='grey', \n", " fontsize=20)\n", "#ergo += text(r'$\\mathscr{E}^-$', (1.4, 0.8), color='grey', \n", "# fontsize=20)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Various remarkable surfaces:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "Rp = exp(1 + sqrt(1-a^2))\n", "Rm = exp(1 - sqrt(1-a^2))\n", "Hp = circle((0,0), Rp, color='black', thickness=2) + \\\n", " text(r'$\\mathscr{H}$', (0.77*Rp, 0.77*Rp), color='black', fontsize=20)\n", "Hm = circle((0,0), Rm, color='green', thickness=2) + \\\n", " text(r'$\\mathscr{H}_{\\rm in}$', (1.2*Rm, 1.05*Rm), color='green', fontsize=20)\n", "R0 = circle((0,0), 1, color='darkorange', linestyle='dotted', thickness=3) + \\\n", " text(r'$r\\!=\\!0$', (1.1,-1.), color='darkorange', fontsize=16)\n", "sing = circle((1,0), 0.1, color='red', fill=True) + \\\n", " circle((-1,0), 0.1, color='red', fill=True)\n", "rminf = circle((0,0), 0.1, edgecolor='black', facecolor='white', fill=True)\n", "region_label = text(r'${\\rm I}$', (-1.2*Rp, 0.8*Rp), fontsize=20) + \\\n", " text(r'${\\rm II}$', (-0.5*Rp, 0.4*Rp), fontsize=20) + \\\n", " text(r'${\\rm III}$', (-0.3*Rm, 0.5*Rm), fontsize=20)\n", "graph = ergo + Hp + Hm + R0 + sing + rminf + region_label" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Carter time machine:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "ft = (r^2+a^2)*(r^2+a^2*costh2) + 2*a^2*r*sinth2" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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b977PmZOTw8mTJzl9+jTVq1cnODiYtm3b6t+4iNwThWUpF1JTU9m9ezeRkZE4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I0bN/L3tX/nFVazuuJ6UB7p2ZSPBq0mMGwSPle3E5D11S3+3/k5vaEEFBMm/S8fyWv+8breoF3P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\nnh8AAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 17 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tmachine = region_plot(ft < 0, (x,-8, 8), (y, -3, 3), incol='yellow', bordercol='gold')\n", "graph += tmachine\n", "show(graph, aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save(\"ker_ergo_a50.pdf\", aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.0.beta0", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }