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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
; | | Date: |
22 Oct 2004 | | Journal: | Prog.Theor.Phys. 113 (2005) 283-303 | | Subject: | gr-qc | | Affiliation: | Kyoto U., Yukawa Inst., Kyoto), Sanjay Jhingan (Basque U., Bilbao), Hiroyuki Nakano (Osaka City U.), Norichika Sago (Osaka U., Dept. Earth Space Sci.), Misao Sasaki (Kyoto U., Yukawa Inst., Kyoto), Takahiro Tanaka (Kyoto U. | | 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 $mu$ orbiting a Schwarzschild black hole of mass $M$, where $mull M$. In our method, we divide the self-force into the $ ilde S$-part and $ ilde R$-part. All the singular behaviors are contained in the $ ilde S$-part, and hence the $ ilde 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 $ ilde S$-part and the $ ilde R$-part required for the construction of sufficiently accurate waveforms for almost circular inspiral orbits. For the regularized $ ilde 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 $ ilde{R}$-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to $ell=13$. | | Source: | arXiv, gr-qc/0410115 | | Services: | Forum | Review | PDF | Favorites | |
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