Finding fields and selfforce in a gauge appropriate to separable wave equations
Abstract
Gravitational waves from the inspiral of a stellarsize 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 blackhole spacetime and on computing the selfforce in a 'radiation gauge.' The gauge is chosen to allow one to compute the perturbed metric from a gaugeinvariant 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 CohenKegeles 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 closedform 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 selfforce from the Teukolsky equation is presented. The method is relatedmore »
 Authors:

 Department of Physics, University of WisconsinMilwaukee, 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 05562821
 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; SPACETIME; SPIN; VECTORS; WAVE EQUATIONS
Citation Formats
Keidl, Tobias S, Friedman, John L, and Wiseman, Alan G. Finding fields and selfforce 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 selfforce 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 selfforce 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 selfforce 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 stellarsize 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 blackhole spacetime and on computing the selfforce in a 'radiation gauge.' The gauge is chosen to allow one to compute the perturbed metric from a gaugeinvariant 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 CohenKegeles 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 closedform 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 selfforce from the Teukolsky equation is presented. The method is related to the Mino, Sasaki, Tanaka and Quinn and Wald (MiSaTaQuWa) renormalization and to the DetweilerWhiting construction of the singular field. It relies on the fact that the renormalized {psi}{sub 0} (or {psi}{sub 4}) is a sourcefree 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 = {05562821},
number = 12,
volume = 75,
place = {United States},
year = {2007},
month = {6}
}