Journal Article

Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild Black Hole

Takahiro Tanaka, Hideyuki Tagoshi and Misao Sasaki

in Progress of Theoretical Physics

Published on behalf of The Physical Society of Japan

Volume 96, issue 6, pages 1087-1101
Published in print December 1996 | ISSN: 0033-068X
Published online December 1996 | e-ISSN: 1347-4081 | DOI: https://dx.doi.org/10.1143/PTP.96.1087
Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild Black Hole

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Using the post-Newtonian (PN) expansion technique of the gravitational wave perturbation around a Schwarzschild black hole, we calculate analytically the energy flux of gravitational waves induced by a particle in circular orbits up to the 5.5PN order, i.e., O(v11) beyond Newtonian. By comparing the formula with numerical data, we find that the error of the 5.5PN formula is about 4% when the particle is on the last stable circular orbit. We also estimate the error ΔN in the total cycle of gravitational waves from coalescing compact binaries in a laser interferometer's band produced by using the post-Newtonian approximations. We find that, as for the neutron star-black hole binaries, the 4.5PN approximation gives ΔN ≲ 1 for a black hole of mass M < 40M, while it gives ΔN ≳ 1 for a black hole of mass M > 40M.

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