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A new analytical method for self-force regularization II. Testing the efficiency for circular orbits

Wataru Hikida·Sanjay Jhingan·Hiroyuki Nakano·Norichika Sago·Misao Sasaki·Takahiro Tanaka
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Abstract

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 $μ$ orbiting a Schwarzschild black hole of mass $M$, where $μ\ll M$. 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 $\ell=13$.

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Wataru Hikida, Sanjay Jhingan, Hiroyuki Nakano, Norichika Sago, Misao Sasaki, Takahiro Tanaka. 2005-03-04. A new analytical method for self-force regularization II. Testing the efficiency for circular orbits. https://doi.org/10.1143/ptp.113.283

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