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

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

1994-12-08

arxiv.org/abs/gr-qc/9412027v1

Phys.Rev.D51:5753-5767,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

ReVTeX, 17 pages

Scientific paper

10.1103/PhysRevD.51.5753

A particle of mass $\mu$ moves on a circular orbit of a nonrotating black hole of mass $M$. Under the restrictions $\mu/M \ll 1$ 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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