• DOI:10.1103/PhysRevD.67.104016
• Corpus ID: 119429833

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

@article{Detweiler2002SelfforceOA,
  title={Self-force of a scalar field for circular orbits about a Schwarzschild black hole},
  author={Steven Lawrence Detweiler and Eirini Messaritaki and Bernard F. Whiting},
  journal={Physical Review D},
  year={2002},
  volume={67},
  pages={104016}
}

• S. Detweiler, E. Messaritaki, B. Whiting
• Published 20 May 2002
• Physics
• Physical Review D

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.