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), weanalytically perform the post-Newtonian expansion of gravitational waves from atest particle in circular orbit of radius $r_0$ around a Schwarzschild blackhole of mass $M$. We calculate gravitational wave forms and luminosity up to$v^8$ order beyond Newtonian, where $v=(M/r_0)^{1/2}$. In particular, we givethe exact analytical values of the coefficients of $\ln v$ terms at $v^6$ and$v^8$ orders in the luminosity and confirm the numerical values obtainedpreviously by the other of us (HT) and Nakamura. Our result is valid in thesmall mass limit of one body and gives an important guideline for thegravitational wave physics of coalescing compact binaries.Comment: 28 pages, (LaTeX), KUNS-126