Self-force of a scalar field for circular orbits about a Schwarzschild black hole

Detweiler, Steven, Messaritaki, Eirini ORCID: https://orcid.org/0000-0002-9917-4160 and Whiting, Bernard F. 2003. Self-force of a scalar field for circular orbits about a Schwarzschild black hole. Physical Review -Series D- 67 (10) , 104016. 10.1103/PhysRevD.67.104016

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Abstract

The foundations are laid for the numerical computation of the actual worldline for a particle orbiting a black hole and emitting gravitational waves. The essential practicalities of this computation are illustrated here for a scalar particle of infinitesimal size and small but finite scalar charge. This particle deviates from a geodesic because it interacts with its own retarded field ψret. A recently introduced Green’s function GS precisely determines the singular part ψS of the retarded field. This part exerts no force on the particle. The remainder of the field ψR=ψret−ψS is a vacuum solution of the field equation and is entirely responsible for the self-force. A particular, locally inertial coordinate system is used to determine an expansion of ψS in the vicinity of the particle. For a particle in a circular orbit in the Schwarzschild geometry, the mode-sum decomposition of the difference between ψret and the dominant terms in the expansion of ψS provide a mode-sum decomposition of an approximation for ψR from which the self-force is obtained. When more terms are included in the expansion, the approximation for ψR is increasingly differentiable, and the mode sum for the self-force converges more rapidly.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Cardiff University Brain Research Imaging Centre (CUBRIC) Medicine
Subjects:	Q Science > QC Physics
Publisher:	American Physical Society
ISSN:	0556-2821
Last Modified:	01 Nov 2022 09:23
URI:	https://orca.cardiff.ac.uk/id/eprint/87757

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