Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole :Effects of Black Hole Absorption

TL;DR

This paper analytically calculates the energy absorption of gravitational waves by a rotating black hole caused by a particle in circular orbit, revealing effects on binary orbital evolution with higher-order velocity terms.

Contribution

It provides a higher-order (up to O((v/c)^8)) analytical calculation of gravitational wave absorption by Kerr black holes, including the effects of black hole rotation.

Findings

Absorption occurs at O((v/c)^5) for rotating black holes, lower than the non-rotating case.

Black hole rotation significantly affects gravitational wave absorption rates.

Results impact understanding of orbital evolution in coalescing binaries.

Abstract

When a particle moves around a Kerr black hole, it radiates gravitational waves.Some of these waves are absorbed by the black hole. We calculate such absorption of gravitational waves induced by a particle of mass mu in a circular orbit on an equatorial plane around a Kerr black hole of mass M. We assume that the velocity of the particle v is much smaller than the speed of light c and calculate the energy absorption rate analytically. We adopt an analytic technique for the Teukolsky equation developed by Mano, Suzuki and Takasugi. We obtain the energy absorption rate to O((v/c)^8) compared to the lowest order. We find that the black hole absorption occurs at O((v/c)^5) beyond the Newtonian-quadrapole luminosity at infinity in the case when the black hole is rotating, which is O((v/c)^3) lower than the non-rotating case. Using the energy absorption rate, we investigate its effects on the orbital evolution of coalescing compact binaries.