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On finding fields and self-force in a gauge appropriate to separable wave equations | | Tobias S. Keidl
; John L. Friedman
; Alan G. Wiseman
; | | Date: |
14 Nov 2006 | | 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 $psi_0$ (or $psi_4$) of the Weyl tensor and follows earlier work by Chrzanowski, and Cohen and Kegeles (we correct an 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 $psi_0$ and $psi_4$ 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 MiSaTaQuWa renormalization and to the Detweiler-Whiting construction of the singular field. It relies on the fact that the renormalized $psi_0$ (or $psi_4$) is a {em sourcefree} solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge. | | Source: | arXiv, gr-qc/0611072 | | Services: | Forum | Review | PDF | Favorites | |
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