{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Using Geodesics (Back-ends & Plotting)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "from einsteinpy.geodesic import Timelike #, Geodesic, Nulllike\n", "from einsteinpy.plotting import GeodesicPlotter, StaticGeodesicPlotter #, InteractiveGeodesicPlotter\n", "\n", "# To ensure plots show up in the documentation\n", "import plotly\n", "plotly.offline.init_notebook_mode()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1: Exploring Schwarzschild Time-like Spiral Capture, using Python Backend and GeodesicPlotter\n", "\n", "### Defining initial conditions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Initial Conditions\n", "position = [4., np.pi / 3, 0.]\n", "momentum = [0., 0., -1.5]\n", "a = 0. # Schwarzschild Black Hole" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating Geodesic" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Geodesic Object:(\n", " Type : (Time-like),\n", " Metric : (Schwarzschild),\n", " Metric Parameters : ((0.0,)),\n", " Initial 4-Position : ([0. 4. 1.04719755 0. ]),\n", " Initial 4-Momentum : ([-0.77055175 0. 0. -1.5 ]),\n", " Trajectory = (\n", " (array([ 0, 1, 2, ..., 15540, 15541, 15542]), array([[ 7.70551750e-04, 3.46410160e+00, -2.16506351e-04, ...,\n", " -5.07812502e-05, 5.41265877e-05, -1.50000000e+00],\n", " [ 1.54110350e-03, 3.46410157e+00, -4.33012700e-04, ...,\n", " -1.01562501e-04, 1.08253176e-04, -1.50000000e+00],\n", " [ 2.31165526e-03, 3.46410152e+00, -6.49519046e-04, ...,\n", " -1.52343754e-04, 1.62379763e-04, -1.50000000e+00],\n", " ...,\n", " [ 2.10892615e+01, 5.06915642e-01, -1.93331152e+00, ...,\n", " -7.67875285e+01, 8.37708122e-01, -1.50000000e+00],\n", " [ 2.11285953e+01, 5.06465005e-01, -1.93307239e+00, ...,\n", " -7.82825155e+01, 8.37749353e-01, -1.50000000e+00],\n", " [ 2.11686915e+01, 5.06014321e-01, -1.93283308e+00, ...,\n", " -7.98370238e+01, 8.37790569e-01, -1.50000000e+00]]))\n", " ),\n", " Output Position Coordinate System = (Cartesian)\n", " ))" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "geod = Timelike(\n", " metric = \"Schwarzschild\",\n", " metric_params = (a,),\n", " position=position,\n", " momentum=momentum,\n", " steps=15543, # As close as we can get before the integration becomes highly unstable\n", " delta=0.0005,\n", " return_cartesian=True,\n", " omega=0.01, # Small omega values lead to more stable integration\n", " suppress_warnings=True, # Uncomment to view the tolerance warning\n", ")\n", "\n", "geod" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting using `GeodesicPlotter`\n", "\n", "Note that `GeodesicPlotter` automatically switches between \"Static\" and \"Interactive\" plots. Since we are in a Jupyter Notebook or Interactive Environment, it uses the \"Interactive\" backend." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "gpl = GeodesicPlotter()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": true }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "colorscale": [ [ 0, "#000" ], [ 1, "#000" ] ], "name": "BH Event Horizon (Outer)", "opacity": 0.75, "showlegend": true, "showscale": false, "type": "surface", "x": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0.12814043996142582, 0.12708840872065935, 0.12394958932224837, 0.11877552109393741, 0.11165116209299053, 0.10269349409723973, 0.09204960176752712, 0.07989425752164034, 0.06642705177604419, 0.05186911567676035, 0.036459490132063226, 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