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

TL;DR

The paper investigates gravitational-wave absorption by a rotating (Kerr) black hole for a test particle in a circular equatorial orbit. It employs the Mano–Suzuki–Takasugi analytic solution of the Teukolsky equation to derive the post-Newtonian expansion of the horizon flux to $O(v^8)$ beyond the infinity luminosity. A key finding is that horizon absorption enters at $O(v^5)$ for rotating BHs, which is $O(v^3)$ lower than in the Schwarzschild case, and can exhibit superradiance with negative energy flux. Applying these results to NS–BH inspirals, the study shows that horizon absorption can modestly affect the orbital evolution, especially for prograde spins and larger BH masses, with important implications for gravitational-wave templates in detectors like LIGO/VIRGO.

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.