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Gravitational radiation from material orbiting a Kerr black hole

Project description


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 Perturbation Toolkit.



This package requires the Python-based free mathematics software system SageMath (at least version 9.3). For versions of SageMath lower than 9.3, only version 0.3.2 of the package will work.

NB: the version of SageMath shipped with Ubuntu 20.04 is only 9.0; instead of the Ubuntu package sagemath, install then the most recent binary for Ubuntu 20.04 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).

NB1 (Ubuntu users): if you have installed SageMath as the system package sagemath (e.g. via apt-get install), the installation is system wide and does not allow to use -pip install at the user level. Install instead SageMath from the most recent binary tar ball for Ubuntu from SageMath download page.

NB2: 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, A&A 627, A92 (2019) (preprint: arXiv:1903.02049)

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