A New Analytical Method for Self-Force Regularization.II : Testing the Efficiency for Circular Orbits(Astrophysics and Relativity)

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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≪M. In our method, we divide the self-force into the S^^∿-part and R^^∿-part. All the singular behavior is contained in the S^^∿-part, and hence the 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 S^^∿-part and the R^^∿-part required for the construction of sufficiently accurate waveforms for almost circular inspiral orbits. We calculate the regularized S^^∿-part for circular orbits to 18th post-Newtonian (PN) order and investigate the convergence of the post-Newtonian expansion. We also study the convergence of the remaining R^^∿-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to ι=13.
理論物理学刊行会の論文
2005-02-25