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

Steven Detweiler, Eirini Messaritaki, and Bernard F. Whiting
Phys. Rev. D 67, 104016 – Published 21 May 2003
PDFExport Citation

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=ψretψS 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.

  • Received 20 February 2003

DOI:https://doi.org/10.1103/PhysRevD.67.104016

©2003 American Physical Society

Authors & Affiliations

Steven Detweiler, Eirini Messaritaki, and Bernard F. Whiting

  • Department of Physics, P.O. Box 118440, University of Florida, Gainesville, Florida 32611-8440

References (Subscription Required)

Click to Expand
Issue

Vol. 67, Iss. 10 — 15 May 2003

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×