{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Visualizing Frame Dragging in Kerr Spacetime\n", "\n", "### Importing required modules" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import astropy.units as u\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from einsteinpy.coordinates import BoyerLindquistDifferential\n", "from einsteinpy.geodesic import Timelike\n", "from einsteinpy.metric import Kerr" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setting up metric and intial conditions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Metric Parameters\n", "M, a = 1.989e30 * u.kg, 0.3 * u.one\n", "\n", "# Coordinate Object\n", "bl = BoyerLindquistDifferential(\n", " t=0. * u.s,\n", " r=49.95e8 * u.m,\n", " theta=np.pi / 2 * u.rad,\n", " phi=np.pi * u.rad,\n", " v_r=0. * u.m / u.s,\n", " v_th=0. * u.rad / u.s,\n", " v_p=0. * u.rad / u.s\n", ")\n", "\n", "# Kerr Metric Object\n", "mk = Kerr(coords=bl, M=M, a=a)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating the geodesic" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "geod = Timelike(metric=mk, coords=bl, end_lambda=33932.90, step_size=1.2)\n", "\n", "ans = geod.trajectory\n", "\n", "x, y = ans[:,1], ans[:,2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the geodesic" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "%matplotlib inline\n", "\n", "fig = plt.figure(figsize=(12,10))\n", "plt.scatter(x, y, s=0.2)\n", "plt.scatter(0, 0)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " As can be seen in the plot above, the test particle is dragged by the Kerr black hole." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 2 }