POST-NEWTONIAN EXPANSION OF GRAVITATIONAL-WAVES FROM A PARTICLE IN SLIGHTLY ECCENTRIC ORBIT AROUND A ROTATING BLACK-HOLE

Using the Teukolsky and Sasaki-Nakamura equations, eve calculate the p ost-Newtonian expansion of the energy and angular momentum luminositie s of gravitational waves from a test particle with slightly eccentric orbit around a rotating black hole up to O(upsilon(5)) beyond the quad rupole formula. We find that circular orbit is stable up through the o rder O(upsilon(5)) even if the spin of a black hole exists. Using the results, we argue the total phase of gravitational waves from coalesci ng compact binaries. We find that the eccentricity is important at O(u psilon(5)) order if the initial eccentricity in the LIGO's band is gre ater than 0.4. There are possibilities that binaries which have a non- negligible eccentricity will be observed by laser interferometers and our results will be useful to analyze gravitational waves from such bi naries.