PostNewtonian expansion of gravitational waves from a particle in circular orbit around a Schwarzschild black hole

Tagoshi, Hideyuki; Sasaki, Misao

doi:10.1143/PTP.92.745

PostNewtonian expansion of gravitational waves from a particle in circular orbit around a Schwarzschild black hole

Hideyuki Tagoshi
(
- Kyoto U.
)
,
Misao Sasaki
(
- Kyoto U.
)

May, 1994

28 pages

Published in:

Prog.Theor.Phys. 92 (1994) 745-772

e-Print:

gr-qc/9405062 [gr-qc]

DOI:

10.1143/PTP.92.745

Report number:

KUNS-1262

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Abstract: (arXiv)

Based upon the formalism recently developed by one of us (MS), we analytically perform the post-Newtonian expansion of gravitational waves from a test particle in circular orbit of radius

r_0

around a Schwarzschild black hole 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 give the 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 obtained previously by the other 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.

black hole: Schwarzschild
particle: orbit
gravitational radiation
luminosity
numerical calculations

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