A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit

TL;DR

This paper presents a fourth-order accurate numerical algorithm for integrating black hole perturbation equations with source terms involving Dirac delta functions, improving precision in modeling gravitational perturbations caused by orbiting particles.

Contribution

The authors develop a novel fourth-order time-domain numerical method for black hole perturbation equations with delta function sources, enabling more accurate simulations.

Findings

Achieved fourth-order convergence in numerical integration.

Re-derived source terms for better waveform definitions.

Facilitated direct metric reconstruction from waveforms.

Abstract

We obtain a fourth order accurate numerical algorithm to integrate the Zerilli and Regge-Wheeler wave equations, describing perturbations of nonrotating black holes, with source terms due to an orbiting particle. Those source terms contain the Dirac's delta and its first derivative. We also re-derive the source of the Zerilli and Regge-Wheeler equations for more convenient definitions of the waveforms, that allow direct metric reconstruction (in the Regge-Wheeler gauge).