h1Lorenz

This repository contains code to compute the first-order (in the mass-ratio) Lorenz-gauge metric perturbation from a particle in a circular orbit about a Schwarzschild black hole.

The code computes the tensor spherical harmonic modes of the metric perturbation and its first radial derivative on a supplied grid of radial values. The spherical harmonic basis used is the Barack-Lousto-Sago basis. This code is a modified version of the code developed for arXiv:1308.5223

Dependencies and compilation

This software needs the GNU Scientific Library, Scons, and OpenMPI to compile and run.

Compile using scons

Usage

First you need to generate an input grid. For this you can use the Mathematica notebook in notebooks/ComputeRadialGrid.nb.

To run the code use:

mpirun -n $numprocs ./h1Lorenz r0 lmax gridfile outdir

where $numprocs should be at least 2 as one core is used to distribute work to the other cores (note: we've not tested how well the code works with n >= 2 in a long time), r0 is the particle's radius (in Schwarzschild coordinates), lmax is the maximum l value to compute, gridfile is the location of the gridfile, and outdir is the output directory.

For example, after runnign the ComputeRadialGrid.nb notebook for r0=8.1 you could run

./mpirun -n 2 15 input/radial_grid_r8.1.h5 data/fields_r8.1/

Output

The code output the all the components of the first-order metric perturbation in the Lorenz gauge. For some modes, some of the asymptotic amplitudes are also computed. The data is saved using the HDF5 format. There is a Mathematica notebook (Loadh1Lorenz.nb) in the notebooks/ subfolder which shows how to read in the data.

In general the l=even, m=0 modes are not computed accurately (or at all) due to long integration regions for the homogeneous solutions. For now and so these should be replaced with another calculation.

Authors

Niels Warburton Sarp Akcay

Papers on related topics

Lorenz-gauge decomposition into tensor spherical harmonics: arXiv:0510019

Lorenz-gauge circular orbits in frequency domain arXiv:1012.5860
Lorenz-gauge eccentric orbits in the frequency domain arXiv:1308.5223, arXiv:1409.4419

Lorenz-gauge circular orbits in time-domain: arXiv:gr-qc/0701069
Lorenz-gauge eccentric orbits in time-domain: arXiv:1002.2386