Perturbative evolution of particle orbits around Kerr black holes: time domain calculation

TL;DR

This paper develops a time domain numerical method to evolve particle orbits around Kerr black holes, incorporating radiation reaction effects, and validates it against previous frequency domain results, enabling more realistic simulations.

Contribution

It introduces a time domain approach for evolving nearly geodesic orbits with radiation reaction, extending previous frequency domain methods.

Findings

Successfully reproduces earlier frequency domain results.

Provides a new time domain framework for generic orbit evolution.

Facilitates realistic modeling of stellar-mass black holes around supermassive black holes.

Abstract

Treating the Teukolsky perturbation equation numerically as a 2+1 PDE and smearing the singularities in the particle source term by the use of narrow Gaussian distributions, we have been able to reproduce earlier results for equatorial circular orbits that were computed using the frequency domain formalism. A time domain prescription for a more general evolution of nearly geodesic orbits under the effects of radiation reaction is presented. This approach can be useful when tackling the more realistic problem of a stellar-mass black hole moving on a generic orbit around a supermassive black hole under the influence of radiation reaction forces.