Numerical gravitational spin-Hall effect

The gravitational spin-Hall effect (GSHE) describes the frequency and spin-dependent trajectories of wavepackets, such as gravitational-waves emitted from a binary black hole merger, propagating in strong gravitational fields as described in [1]. In this package, we calculate the GSHE-induced deviations from a null geodesic and the observed detector strain for a gravitational wavepacket as introduced in [2, 3].

Installation

The package is split amongst three parts:

1. GSHEIntegrator.jl: Julia code for numerically solved the GSHE equations of motion for a wavepacket in a Kerr spacetime.
2. GSHESymbolical: Mathematica code for the symbolic derivation of the GSHE equations of motion, which are translated to Julia to be used in GSHEIntegrator.jl.
3. GSHEWaveform: Python code for the calculation of the effect of the GSHE on the detector strain.

The Julia and Python code can be installed following the instructions below, while the Mathematica code are just self-contained notebooks.

First, clone the repository:

git clone git@github.com:Richard-Sti/GSHE.git

To install GSHEIntegrator.jl:

cd GSHE/GSHEIntegrator
julia

Then, in the Julia REPL, enter the package manager mode by pressing ] and type:

dev .
precompile

This will install the package in development along with its dependencies. To test the installation, you may run in the Julia REPL:

using GSHEIntegrator

To instead install GSHEWaveform and create a new virtual environment:

# Move to the GSHE
cd GSHE

# Create a new virtual environment
python -m venv venv_gshe
source venv_gshe/bin/activate
python -m pip install --upgrade pip && python -m pip install --upgrade setuptools

# Finally install the cloned package
python -m pip install -e .

Examples

For an example Julia notebook on how to compute trajectories from an observer or find connecting trajectories between the source and observer, see GSHE/scripts/example_trajectories.ipynb.

Things to be resolved later

• GW emitter anisotropy
• Look into precompilation.
• Why does the code sometimes struggle to find solutions? Too many iterations near the horizon?
• Asymptotic behaviour far from source need better understood?

License and Citation

If you use or find useful any of the code in this repository, please cite [2, 3].

Copyright (C) 2024 Richard Stiskalek, Marius Oancea, Miguel Zumalacarregui
This program is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General
Public License for more details.

You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.

Contributors

• Richard Stiskalek (University of Oxford)
• Marius Oancea (University of Vienna)
• Miguel Zumalacárregui (Max Planck Institute for Gravitational Physics)

References

[1] Andersson, Lars, Jérémie Joudioux, Marius A. Oancea, and Ayush Raj. "Propagation of polarized gravitational waves." Physical Review D 103, no. 4 (2021): 044053.

[2] Marius A. Oancea, Richard Stiskalek, and Miguel Zumalacárregui. "Frequency- and polarization-dependent lensing of gravitational waves in strong gravitational fields." Physical Review D 109 (2024): 124045

[3] Marius A. Oancea, Richard Stiskalek, and Miguel Zumalacárregui. "Probing general relativistic spin-orbit coupling with gravitational waves from hierarchical triple systems." arXiv:2307.01903