Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild Black Hole : 5.5 Post-Newtonian Formula : Astrophysics and Relativity

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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., ο(υ^<11>) 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 ΔΝ 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 ΔΝ ≲ 1 for a black hole of mass M < 40M_⊙, while it gives ΔΝ ≲ 1 for a black hole of mass M > 40M_⊙.
理論物理学刊行会の論文
1996-12-25