2006/11/30 by Tobias S. Keidl, Tobias Keidl, John L. Friedman +2 · 2 citations
Engineering · Physics and Astronomy · #Angular momentum #Astrophysical Phenomena and Observations #Black hole (networking) #Classical mechanics #Experimental and Theoretical Physics Studies #Gauge fixing #Gauge theory #General relativity #Geophysics and Sensor Technology #Gravitation #Gravitational field #Gravitational wave #Lorenz gauge condition #Mathematical physics #Physics #Point particle #Quantum electrodynamics #Quantum mechanics #Renormalization #Rotating black hole #Schwarzschild metric #Schwarzschild radius #Spacetime #gr-qc
paper · pdf · doi:10.1103/physrevd.75.124009
published as Phys.Rev.D75:124009,2007 · 58 pages, 5 tables, typographical errors corrected
arxiv created 2007/05/29 · openalex publication_date 2007/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \ensuremathψ0 (or \ensuremathψ4) 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 \ensuremathψ0 and \ensuremathψ4 are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin \ifmmode±\else\textpm\fi2 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 \ensuremathψ0 (or \ensuremathψ4) is a source-free solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge.