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

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.