pybhpt

A python package for solving problems in black hole perturbation theory.

pybhpt is a collection of numerical tools for analyzing perturbations of Kerr spacetime, particularly the self-forces and metric-perturbations experienced by small bodies moving in a Kerr background. Subpackages include:

• pybhpt.geodesic: a module that generates bound periodic timelike geodesics in Kerr spacetime
• pybhpt.radial: a module that calculates homogeneous solutions of the radial Teukolsky equation
• pybhpt.swsh: a module that constructs the spin-weighted spheroidal harmonics
• pybhpt.teuk: a module that evaluates the inhomogeneous solutions (Teukolsky amplitudes) of the radial Teukolsky equation due to a point-particle on a bound timelike Kerr geodesic
• pybhpt.flux: a module that produces the gravitational wave fluxes sourced by a point-particle on a generic bound timelike Kerr geodesic
• pybhpt.hertz: a module that solves for the Hertz potentials for the CCK and AAB metric reconstruction procedures
• pybhpt.metric: a module that produces the coefficients needed to reconstruct the metric from the Hertz potentials
• pybhpt.redshift: a module that computes the generalized Detweiler redshift invariant in a variety of gauges

See the Documentation pages for more information about the package, including User Guides and API. References and author information can be found at the bottom of the README.

Quick Installation

Tagged releases of pybhpt are available as wheel packages for macOS and 64-bit Linux on PyPI. Install using pip:

python3 -m pip install pybhpt

Developer Installation

pybhpt relies on several dependencies to install and run, namely a C/C++ compiler (e.g., g++), gsl, boost, Cython, numpy, scipy, and python >= 3.8. To reduce package conflicts and ensure that the proper dependencies are installed, we recommend using conda (paricularly through Miniforge) and its virtual environments.

To create a conda environment pybhpt-env with just the necessary dependencies use environment.yml:

conda env create -f environment.yml
conda activate pybhpt-env

For an environment with the extended recommended software dependencies, one can replace environment.yml with environment-extended.yml or follow the extended pip install instructions below.

Next clone the pybhpt repository from GitHub:

git clone https://github.com/znasipak/pybhpt.git
cd pybhpt

The boost repository is included as a submodule under extern/boost. To activate the submodule:

git submodule update --init --recursive extern/boost

To include the Boost headers in the compilation path:

cd extern/boost
chmod +x bootstrap.sh
./bootstrap.sh
./b2 headers

Finally, we recommend installing the package via pip:

pip install .

or to get the basic development dependencies:

pip install '.[dev, testing]'

To get all recommended software:

pip install '.[dev, testing, extended]'

To ensure the package installed properly, run the unit tests via pytest:

pytest .

Conda Environments with Jupyter

To run the code in a Jupyter notebook, we recommend pip installing the following dependencies:

pip install ipykernel matplotlib

These dependencies are already included in environment-extended.yml or in the optional pip install dependencies. To make the environment accessible within Jupyter:

python -m ipykernel install --user --name=pybhpt-env

Uninstalling

If the package is installed using pip, then one can easily uninstall the package by executing

pip uninstall pybhpt

Developers may also need to remove the directories build/ and pybhpt.egg.info/ from the main repository.

Troubleshooting compiling from source

If there are problems compiling pybhpt from source, it may be because cmake cannot identify the correct compiler. To fix this issue, one can try to explicitly download the necessary compiler into their conda environment.

To include the necessary compiler on macOS Intel:

conda install clang_osx-64 clangxx_osx-64

To include the necessary compiler on macOS arm/silicon:

conda install clang_osx-arm64 clangxx_osx-arm64

To include the necessary compiler on Linux:

conda install gcc_linux-64 gxx_linux-64

References

Theoretical background for the code and explanations of the numerical methods used within are summarized in the references below:

• Z. Nasipak, Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit (2025) arXiv:2507.07746
• Z. Nasipak, An adiabatic gravitational waveform model for compact objects undergoing quasi-circular inspirals into rotating massive black holes, Phys. Rev. D 109, 044020 (2024) arXiv:2310.19706
• Z. Nasipak, Adiabatic evolution due to the conservative scalar self-force during orbital resonances, Phys. Rev. D 106, 064042 (2022) arXiv:2207.02224

Authors

Zachary Nasipak

Contributors

Zachary Nasipak

Christian Chapman-Bird