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

Shah, A., Keidl, T., Friedman, J., Kim, D.-H., & Price, L. (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. doi:10.1103/PhysRevD.83.064018.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-08F7-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-08F8-D
Genre: Journal Article

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1009.4876 (Preprint), 297KB
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 Creators:
Shah, Abhay, Author
Keidl, Tobias, Author
Friedman, John, Author
Kim , Dong-Hoon1, Author
Price, Larry, Author
Affiliations:
1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
 Abstract: 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. 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_{\alpha\beta} u^\alpha u^\beta (= h_{uu}) must have the same value for our radiation gauge as for a Lorenz gauge; and we confirm this numerically to one part in 10^{13}. As outlined in the first paper, the perturbed metric is constructed from a Hertz potential that is in term obtained algebraically from the the retarded perturbed spin-2 Weyl scalar, \psi_0 . We use a mode-sum renormalization and find the renormalization coefficients by matching a series in L = \ell + 1/2 to the large-L behavior of the expression for the self-force in terms of the retarded field h_{\alpha\beta}^{ret}; we similarly find the leading renormalization coefficients of h_{uu} 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_{\alpha} \propto < \nabla_\alpha \rho^{-1}>, the part of \nabla_\alpha \rho^{-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 \rho.

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 Dates: 2010-09-242011-03-072011
 Publication Status: Published in print
 Pages: 21 pages, 2 figures
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1009.4876
DOI: 10.1103/PhysRevD.83.064018
URI: http://arxiv.org/abs/1009.4876
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : Published for the American Physical Society by the American Institute of Physics
Pages: - Volume / Issue: 83 (6) Sequence Number: 064018 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258