{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frame Dragging in Kerr Spacetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from astropy import units as u\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from einsteinpy.metric import Kerr\n",
    "from einsteinpy.coordinates import BoyerLindquistDifferential\n",
    "from einsteinpy.bodies import Body\n",
    "from einsteinpy.geodesic import Geodesic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0.3 * u.m\n",
    "Attractor = Body(name=\"BH\", mass=1.989e30 * u.kg, a=a)\n",
    "init_conditions = BoyerLindquistDifferential(49.95e5 * u.km, np.pi / 2 * u.rad, \n",
    "                                             np.pi * u.rad, 0 * u.km / u.s, \n",
    "                                             0 * u.rad / u.s, 0 * u.rad / u.s,\n",
    "                                             a)\n",
    "Particle = Body(differential=init_conditions, parent=Attractor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "geodesic = Geodesic(body=Particle, time=0 * u.s, end_lambda=33932.90, \n",
    "                    step_size=1.2, metric=Kerr)\n",
    "ans = geodesic.trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y = ans[:,1], ans[:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plt.scatter(x,y, s=0.2)\n",
    "plt.scatter(0,0, )\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}