{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Meridional plots in Kerr spacetime for $a/m=0.99$" ] }, { "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 + 0.980100000000000*y^2/(x^2 + y^2) - log(x^2 + y^2)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = 0.99\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, -5, 5), 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'$\\mathscr{E}^+$', (1.05*e^2, 0.5*e), color='grey', \n", " fontsize=20)\n", "ergo += text(r'$\\mathscr{E}^-$', (1.5, 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'$\\mathscr{H}$', (0.84*Rp, 0.77*Rp), color='black', fontsize=20)\n", "Hm = circle((0,0), Rm, color='green', thickness=2) + \\\n", " text(r'$\\mathscr{H}_{\\rm in}$', (0.75*Rm, 0.9*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'${\\rm I}$', (-2.3*Rp, Rp), fontsize=20) + \\\n", " text(r'${\\rm II}$', (-0.72*Rp, 0.5*Rp), fontsize=20) + \\\n", " text(r'${\\rm III}$', (-0.4*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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Qm5sLX19fTJ06FZaWltoui0jnMTz0UYWFhdizZw/q6uowevRo2NnZcS5sopug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\nej79+OOP6uvr0zfffNPpoUCva6vdMTus2Wxqc3NT2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"text/plain": [ "Graphics object consisting of 18 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tmachine = region_plot(ft < 0, (x,-2, 2), (y, -2, 2), 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_a99.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 }