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Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a radiation gauge

Shah, Abhay G. and Keidl, Tobias S. and Friedman, John L. and Kim, Dong-Hoon and Price, Larry R. (2011) Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a radiation gauge. Physical Review D, 83 (6). 064018. ISSN 2470-0010.

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This is the second of two companion papers on computing the self-force in a radiation gauge; more precisely, the method uses a radiation gauge for the radiative part of the metric perturbation, together with an arbitrarily chosen gauge for the parts of the perturbation associated with changes in black-hole mass and spin and with a shift in the center of mass. In a test of the method delineated in the first paper, we compute the conservative part of the self-force for a particle in circular orbit around a Schwarzschild black hole. The gauge vector relating our radiation gauge to a Lorenz gauge is helically symmetric, implying that the quantity h_(αβ)u^(α)u^(β) must have the same value for our radiation gauge as for a Lorenz gauge; and we confirm this numerically to one part in 10^(14). As outlined in the first paper, the perturbed metric is constructed from a Hertz potential that is in a term obtained algebraically from the retarded perturbed spin-2 Weyl scalar, ψ_(0)^(ret). We use a mode-sum renormalization and find the renormalization coefficients by matching a series in L= ℓ + 1/2 to the large-L behavior of the expression for the self-force in terms of the retarded field h_(αβ)^(ret); we similarly find the leading renormalization coefficients of h_(αβ)u^(α)u^(β) and the related change in the angular velocity of the particle due to its self-force. We show numerically that the singular part of the self-force has the form f^(S)_(α) = <∇_(α)ρ^(-1)>, the part of ∇_(α)ρ^(-1) that is axisymmetric about a radial line through the particle. This differs only by a constant from its form for a Lorenz gauge. It is because we do not use a radiation gauge to describe the change in black-hole mass that the singular part of the self-force has no singularity along a radial line through the particle and, at least in this example, is spherically symmetric to subleading order in ρ.

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Additional Information:© 2011 American Physical Society. Received 7 October 2010; published 15 March 2011. We thank N. Sago for corrections and helpful comments and E. Messaritaki for a number of discussions early in the course of the work on this paper and paper I. This work was supported in part by NSF Grant Nos. PHY 0503366 and PHY 1001515. D. H-K’s work was supported by the Alexander von Humboldt Foundation’s Sofja Kovalevskaja Programme funded by the German Federal Ministry of Education and Research and by WCU (World Class University) program of NRF/MEST under Contract No. R32-2009-000-10130-0.
Funding AgencyGrant Number
NSFPHY 0503366
NSFPHY 1001515
Alexander von Humboldt Foundation Sofja Kovalevskaja ProgrammeUNSPECIFIED
German Federal Ministry of Education and ResearchUNSPECIFIED
NRF/MEST World Class University Program (WCU)R32-2009-000-10130-0
Issue or Number:6
Classification Code:PACS: 04.30.Db, 04.25.Nx, 04.70.Bw
Record Number:CaltechAUTHORS:20110405-111043563
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23244
Deposited By: Jason Perez
Deposited On:10 Apr 2011 04:08
Last Modified:03 Oct 2019 02:44

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