{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Visualizing Precession in Schwarzschild Spacetime\n",
"\n",
"### Importing required modules"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"from einsteinpy.geodesic import Timelike\n",
"from einsteinpy.plotting.geodesic import GeodesicPlotter"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Setting up the system\n",
" - Initial position & momentum of the test partcle\n",
" - Spin of the Schwarzschild Black Hole (= 0)\n",
" - Other solver parameters\n",
" \n",
"Note that, we are working in _M_-Units ($G = c = M = 1$). Also, since the Schwarzschild spacetime has spherical symmetry, the values of the angular components do not affect the end result (We can always rotate our coordinate system to bring the geodesic in the equatorial plane). Hence, we set $\\theta = \\pi / 2$ (equatorial plane), with initial $p_\\theta = 0$, which implies, that the geodesic should stay in the equatorial plane."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"position = [40, np.pi / 2, 0.]\n",
"momentum = [0., 0., 4.]\n",
"a = 0.\n",
"end_lambda = 20000.\n",
"step_size = 0.5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Calculating the geodesic, using the Julia back-end"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"geod = Timelike(\n",
" position=position,\n",
" momentum=momentum,\n",
" a=a,\n",
" end_lambda=end_lambda,\n",
" step_size=step_size,\n",
" return_cartesian=True,\n",
" julia=True\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting the geodesic"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
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"output_type": "display_data"
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