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geodpy

This code aims to simulate geodesics given an arbitrary space-time metric.

Capabilities

  • Calculate symbolic geodesics
  • Solve the trajectory of a body given an arbitrary metric and symbolic geodesics.
  • Calculate the norm of the velocity of a body.
  • Plot the trajectories on matplotlib in both 2D and 3D.

Requirements

  • matplotlib
  • sympy
  • scipy
  • numpy

You can install these dependencies using:

pip install matplotlib numpy scipy sympy

Installation

Clone the repository and go to the main folder geodpy_lib. You can use these commands:

git clone https://github.com/Sneaker679/geodpy_lib
cd geodpy_lib

In order to be able to import the classes and functions of this library, you will need to add the geodpy_lib folder to your PYTHON PATH. If you are already located in this folder, you can run the following command.

export PYTHONPATH="$(pwd):$PYTHONPATH"

To add the folder permanently to your PYTHON PATH, run this command instead.

echo 'export PYTHONPATH="$HOME'${PWD/#$HOME/}':$PYTHONPATH"' >> $HOME/.bashrc

or, for zsh terminals, run this.

echo 'export PYTHONPATH="$HOME'${PWD/#$HOME/}':$PYTHONPATH"' >> $HOME/.zshrc

Basic Usage -> Using the examples

Example with the Schwarzschild metric

In the geodpy_lib/examples/schwarzschild folder, run any of the python files except for schwarzschild.py (since it acts as a module for the other files). For instance, you could run:

python3 near_horizon.py

which will run a configuration of the Schwarzschild metric where the body in orbit is very close to the event horizon of the Schwarzschild black hole. A plot should be displayed on the screen using matplotlib.

Structure of the examples

With the last example in mind, here is a more detailed overlook of how the examples are structured. This section will make it easier to understand how you can customize the orbits to your liking and experiment with the code.

In the examples folder are many examples that simulate geodesics with varied metrics, including the Schwarzschild, Kerr and Schwarzschild de Sitter metric. All these folders work in the same way. Taking the schwarzschild folder as an example, inside it are many files, the main one being schwarzschild.py. This script acts as a python module for the other files. Inside this code, there is a schwarzschild() function, which you can call with varied parameters to generate different geodesics. The other files in the schwarzschild folder are simple sripts who call the schwarzschild() function with different initial values. As it was shown in the previous section, the near_horizon.py script, for example, yields a geodesic simulated near the event horizon of a non rotating Schwarzschild blackhole. You can run the other examples in the other folders the same way.

The README inside each example folders specifies the meaning of the constants and quantities used.

Advanced Usage

For more advance usages, refer to geodpy_lib/docs/HowTo_trajectories.md, geodpy_lib/docs/HowTo_coordinates.md and geodpy_lib/docs/HowTo_plotters.md

Interface

If you wish to see a more detailed overview of all the classes and functions at your disposition, be sure to checkout the geodpy_lib/docs/class_documentation/. There are many Markdown files there explaining how all the classes and functions work. The REAMDEs in this folder also specify how you can import them.