Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbit around a Schwarzschild Black Hole

Abstract

Based upon the formalism recently developed by one of us (MS), we analytically perform the post-Newtonian expansion of gravitational w;;tves from a test particle in circular orbit of radius ro around a Schwarzschild black hole of mass M. We calculate gravitational wave forms and luminos­ ity up to v 8 order beyond Newtonian, where v=(M/ro) 112 • In particular, we give the exact analytical values of the coefficients of In v terms at v 6 and v 8 orders in the luminosity and confirm the numerical values obtained previously by one of us (HT) and Nakamura. Our result is valid in the small mass limit of one body and gives an important guideline for the .gravitational wave physics of coalescing compact binaries.