Gravitational waves from a point particle in circular orbit around a black hole: Logarithmic terms in the post-Newtonian expansion.

Abstract

We find logarithmic terms in a post-Newtonian expansion of gravitational radiation induced by a particle traveling a circular orbit of radius ${\mathit{r}}_{0}$ around a Schwarzschild black hole of mass M. We calculate the gravitational wave luminosity using the Teukolsky equation to high accuracy (\ensuremath{\sim}20 figures) and determine the coefficients of the post-Newtonian expansion by means of least squares fitting. We find that there are terms proportional to ${\mathit{x}}^{6}$lnx and ${\mathit{x}}^{8}$lnx where x=(M/${\mathit{r}}_{0}$${)}^{1/2}$. We also examine the accumulated phase of coalescing compact star binaries by means of the post-Newtonian expansion as it sweeps through the bandwidth at which the future laser interferometric detectors have good sensitivity.