Gravitational radiation from a particle in circular orbit around a black hole. V. Black-hole absorption and tail corrections

Abstract

A particle of mass $\hat{I}¼$ moves on a circular orbit of a nonrotating black hole of mass $M$. Under the restrictions $\hat{I}¼/M\ll 1$ and $v\ll 1$, where $v$ is the orbital velocity, we consider the gravitational waves emitted by such a binary system. We calculate $\dot{E}$, the rate at which the gravitational waves remove energy from the system. The total energy loss is given by $\dot{E}={\dot{E}}^{\infty }+{\dot{E}}^H$, where ${\dot{E}}^{\infty }$ denotes that part of the gravitational-wave energy which is carried off to infinity, while ${\dot{E}}^H$ denotes the part which is absorbed by the black hole. We show that the black-hole absorption is a small effect: ${\dot{E}}^H/\dot{E}\simeq v^8$. We also compare the wave generation formalism which derives from perturbation theory to the post-Newtonian formalism of Blanchet and Damour. Among other things we consider the corrections to the asymptotic gravitational-wave field which are due to wave-propagation (tail) effects.

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