Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-10-22
Prog.Theor.Phys.113:283-303,2005
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
21pages, 12 figures
Scientific paper
10.1143/PTP.113.283
In a previous paper, based on the black hole perturbation approach, we formulated a new analytical method for regularizing the self-force acting on a particle of small mass $\mu$ orbiting a Schwarzschild black hole of mass $M$, where $\mu\ll M$. In our method, we divide the self-force into the $\tilde S$-part and $\tilde R$-part. All the singular behaviors are contained in the $\tilde S$-part, and hence the $\tilde R$-part is guaranteed to be regular. In this paper, focusing on the case of a scalar-charged particle for simplicity, we investigate the precision of both the regularized $\tilde S$-part and the $\tilde R$-part required for the construction of sufficiently accurate waveforms for almost circular inspiral orbits. For the regularized $\tilde S$-part, we calculate it for circular orbits to 18 post-Newtonian (PN) order and investigate the convergence of the post-Newtonian expansion. We also study the convergence of the remaining $\tilde{R}$-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to $\ell=13$.
Hikida Wataru
Jhingan Sanjay
Nakano Hiroyuki
Sago Norichika
Sasaki Misao
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