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

We find logarithmic terms in a post-Newtonian expansion of gravitational radiation induced by a particle traveling a circular orbit of radius r₀ around a Schwarzschild black hole of mass M. We calculate the gravitational wave luminosity using the Teukolsky equation to high accuracy ({~}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 x⁶lnx and x⁸lnx where x=(M/r₀{)}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.