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 post-Newtonian expansion of the energy and angular momentum luminosities of gravitational waves from a test particle with slightly eccentric orbit around a rotating black hole up to O(upsilon(5)) beyond the quadrupole formula. We find that circular orbit is stable up through the order O(upsilon(5)) even if the spin of a black hole exists. Using the results, we argue the total phase of gravitational waves from coalescing compact binaries. We find that the eccentricity is important at O(upsilon(5)) order if the initial eccentricity in the LIGO's band is greater 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 binaries.