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 (approximately 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 x 8lnx 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.