Gravitational radiation from material orbiting a Kerr black hole
Project description
kerrgeodesic_gw
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.
Installation
Requirements
This package requires the Pythonbased 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).
NB1 (Ubuntu users): if you have installed SageMath as the system package sagemath
(e.g. via aptget 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 https://github.com/BlackHolePerturbationToolkit/kerrgeodesic_gw.git
This creates a directory kerrgeodesic_gw
.
Run
sage pip install upgrade noindex 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 https://github.com/BlackHolePerturbationToolkit/kerrgeodesic_gw.git
sage pip install user upgrade noindex 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 noindex v e kerrgeodesic_gw
or equivalently
cd kerrgeodesic_gw
make develop
Usage
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)
Tests
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
Documentation
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
kerrgeodesic_gw/docs/build/html/index.html
For the LaTeX documentation, use
make docpdf
The pdf reference manual is then
kerrgeodesic_gw/docs/build/latex/kerrgeodesic_gw.pdf
Online documentation

Article describing the formulas implemented in the package (open access)

Demo notebooks:

For the tensor calculus functionalities of the KerrBH class provided by the package, see these examples: Kerr 1, Kerr 2, Kerr 3, and more generally SageManifolds documentation.
Authors
 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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