POST-NEWTONIAN EXPANSION OF GRAVITATIONAL-WAVES FROM A PARTICLE IN CIRCULAR ORBIT AROUND A SCHWARZSCHILD BLACK-HOLE

Based upon the formalism recently developed by one of us (MS), we anal ytically perform the post-Newtonian expansion of gravitational waves f rom a test particle in circular orbit of radius gamma0 around a Schwar zschild black hole of mass M. We calculate gravitational wave forms an d luminosity up to upsilon8 order beyond Newtonian, where upsilon = (M /r0)1/2. In particular, we give the exact analytical values of the coe fficients of ln upsilon terms at upsilon6 and upsilon8 orders in the l uminosity and confirm the numerical values obtained previously by one of us (HT) and Nakamura. Our result is valid in the small mass limit o f one body and gives an important guideline for the gravitational wave physics of coalescing compact binaries.