Point particle orbiting a Schwarzschild black hole: Phase-integral analysis of the gravitational radiation emitted.

Abstract

An approximate formula for the luminosity of gravitational waves generated by a point particle in circular orbit around a Schwarzschild black hole is derived using the phase-integral method. A comparison between numerical results obtained from this formula and recent numerical integration results of Cutler et al. shows that the approximate approach is relatively accurate for the higher values of $m$ and each $\ensuremath{\ell}$. Moreover, the accuracy increases with increasing $\ensuremath{\ell}$. For the quadrupole contribution that dominates the radiation the phase-integral formula suffers from a systematic error of roughly 1.5% for large orbital radii, however. At the same time, the higher multipole contributions agree perfectly with those obtained by Cutler et al.