On finding fields and self-force in a gauge appropriate to separable wave equations

dc.creatorKeidl, Tobias S.
dc.creatorFriedman, John L.
dc.creatorWiseman, Alan G.
dc.date2006-11-14
dc.date2007-05-29
dc.date.accessioned2026-07-07T10:37:04Z
dc.date.available2026-07-07T10:37:04Z
dc.descriptionGravitational 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 $ψ_0$ (or $ψ_4$) of the Weyl tensor and follows earlier work by Chrzanowski and 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 $ψ_0$ and $ψ_4$ are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin $\pm 2$ 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 $ψ_0$ (or $ψ_4$) is a {\em sourcefree} solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge.
dc.description58 pages, 5 tables, typographical errors corrected
dc.identifierhttps://arxiv.org/abs/gr-qc/0611072
dc.identifierhttp://arxiv.org/abs/gr-qc/0611072
dc.identifierPhys.Rev.D75:124009,2007
dc.identifierdoi:10.1103/PhysRevD.75.124009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180257
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleOn finding fields and self-force in a gauge appropriate to separable wave equations
dc.typetext

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