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Title: Finding fields and self-force in a gauge appropriate to separable wave equations

Abstract

Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and gravitational field of a point particle in a black-hole spacetime and on computing the self-force in a 'radiation gauge.' The gauge is chosen to allow one to compute the perturbed metric from a gauge-invariant component {psi}{sub 0} (or {psi}{sub 4}) of the Weyl tensor and follows earlier work by Chrzanowski, Cohen, and Kegeles (we correct a minor, but propagating, error in the Cohen-Kegeles formalism). The electromagnetic field tensor and vector potential of a static point charge and the perturbed gravitational field of a static point mass in a Schwarzschild geometry are found, surprisingly, to have closed-form expressions. The gravitational field of a static point charge in the Schwarzschild background must have a strut, but {psi}{sub 0} and {psi}{sub 4} are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin {+-}2 parts of the perturbed metric are smooth. Finally a method for finding the renormalized self-force from the Teukolsky equation is presented. The method is relatedmore » to the Mino, Sasaki, Tanaka and Quinn and Wald (MiSaTaQuWa) renormalization and to the Detweiler-Whiting construction of the singular field. It relies on the fact that the renormalized {psi}{sub 0} (or {psi}{sub 4}) is a source-free solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge.« less

Authors:
; ;  [1]
  1. Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201 (United States)
Publication Date:
OSTI Identifier:
20933322
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 75; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.75.124009; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; ELECTROMAGNETIC FIELDS; ERRORS; GAUGE INVARIANCE; GEOMETRY; GRAVITATIONAL FIELDS; GRAVITATIONAL WAVES; MASS; MATHEMATICAL SOLUTIONS; POINT CHARGE; POTENTIALS; RENORMALIZATION; SPACE-TIME; SPIN; VECTORS; WAVE EQUATIONS

Citation Formats

Keidl, Tobias S, Friedman, John L, and Wiseman, Alan G. Finding fields and self-force in a gauge appropriate to separable wave equations. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.124009.
Keidl, Tobias S, Friedman, John L, & Wiseman, Alan G. Finding fields and self-force in a gauge appropriate to separable wave equations. United States. https://doi.org/10.1103/PHYSREVD.75.124009
Keidl, Tobias S, Friedman, John L, and Wiseman, Alan G. Fri . "Finding fields and self-force in a gauge appropriate to separable wave equations". United States. https://doi.org/10.1103/PHYSREVD.75.124009.
@article{osti_20933322,
title = {Finding fields and self-force in a gauge appropriate to separable wave equations},
author = {Keidl, Tobias S and Friedman, John L and Wiseman, Alan G},
abstractNote = {Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and gravitational field of a point particle in a black-hole spacetime and on computing the self-force in a 'radiation gauge.' The gauge is chosen to allow one to compute the perturbed metric from a gauge-invariant component {psi}{sub 0} (or {psi}{sub 4}) of the Weyl tensor and follows earlier work by Chrzanowski, Cohen, and Kegeles (we correct a minor, but propagating, error in the Cohen-Kegeles formalism). The electromagnetic field tensor and vector potential of a static point charge and the perturbed gravitational field of a static point mass in a Schwarzschild geometry are found, surprisingly, to have closed-form expressions. The gravitational field of a static point charge in the Schwarzschild background must have a strut, but {psi}{sub 0} and {psi}{sub 4} are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin {+-}2 parts of the perturbed metric are smooth. Finally a method for finding the renormalized self-force from the Teukolsky equation is presented. The method is related to the Mino, Sasaki, Tanaka and Quinn and Wald (MiSaTaQuWa) renormalization and to the Detweiler-Whiting construction of the singular field. It relies on the fact that the renormalized {psi}{sub 0} (or {psi}{sub 4}) is a source-free solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge.},
doi = {10.1103/PHYSREVD.75.124009},
url = {https://www.osti.gov/biblio/20933322}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 12,
volume = 75,
place = {United States},
year = {2007},
month = {6}
}