Skip to content
A SageMath package to compute gravitational radiation from bodies orbiting a Kerr black hole
Branch: master
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.


A SageMath package to compute gravitational radiation from material orbiting a Kerr black hole

This package makes use of SageMath functionalities developed through the SageManifolds project and is part of the Black Hole Peturbation Toolkit.



This package requires the Python-based free mathematics software system SageMath (at least version 8.2).

NB: the version of SageMath shipped with Ubuntu 18.04 is only 8.1; instead of the Ubuntu package sagemath, install then the most recent binary for Ubuntu 18.04 from SageMath download page.

Simple installation from PyPI

It suffices to run

sage -pip install kerrgeodesic_gw

to have the package ready to use in SageMath. See however install from source below if you want to build a local version of the documentation or modify the source files (development).

NB: on the CoCalc cloud computing platform, you need to add the option --user, i.e. open a terminal and run

sage -pip install --user kerrgeodesic_gw

Here is the kerrgeodesic_gw page on PyPI (the Python Package Index).

Install from source

Download the source from the git repository:

git clone

This creates a directory kerrgeodesic_gw.


sage -pip install --upgrade --no-index -v kerrgeodesic_gw

to install the package in SageMath. A shortcut of the above command is provided by the Makefile distributed with the package:

cd kerrgeodesic_gw
make install

NB: on CoCalc, you need to add the option --user, i.e. open a terminal and run

git clone
sage -pip install --user --upgrade --no-index -v kerrgeodesic_gw

Install for development

If you plan to edit the package source, you should add the option -e to the pip install, i.e. run

sage -pip install --upgrade --no-index -v -e kerrgeodesic_gw

or equivalently

cd kerrgeodesic_gw
make develop


Once the package is installed, you can use it in SageMath, like for instance:

sage: from kerrgeodesic_gw import spin_weighted_spherical_harmonic
sage: theta, phi = var('theta phi')
sage: spin_weighted_spherical_harmonic(-2, 2, 1, theta, phi)
1/4*(sqrt(5)*cos(theta) + sqrt(5))*e^(I*phi)*sin(theta)/sqrt(pi)


This package is configured for tests written in the documentation strings of the source files, also known as doctests. You may then test the install by running, from the root of the package tree (i.e. the directory kerrgeodesic_gw created by the git clone),

sage -t kerrgeodesic_gw

You should then get the message All tests passed!

Alternatively, you can run (from the same directory)

make test


The package documentation can be generated using SageMath's Sphinx installation:

cd docs
sage -sh -c "make html"

A shorthand of the above is

make doc

The html reference manual is then at


For the LaTeX documentation, use

make doc-pdf

The pdf reference manual is then


Online documentation


  • Eric Gourgoulhon
  • Alexandre Le Tiec
  • Frederic Vincent
  • Niels Warburton

Reference: E. Gourgoulhon, A. Le Tiec, F. H. Vincent & N. Warburton: Gravitational waves from bodies orbiting the Galactic Center black hole and their detectability by LISA, arXiv:1903.02049

You can’t perform that action at this time.
You signed in with another tab or window. Reload to refresh your session. You signed out in another tab or window. Reload to refresh your session.