Regularization of fields for self-force problems in curved spacetime: Foundations and a time-domain application
Dec, 2007Citations per year
Abstract: (arXiv)
We propose an approach for the calculation of self-forces, energy fluxes and waveforms arising from moving point charges in curved spacetimes. As opposed to mode-sum schemes that regularize the self-force derived from the singular retarded field, this approach regularizes the retarded field itself. The singular part of the retarded field is first analytically identified and removed, yielding a finite, differentiable remainder from which the self-force is easily calculated. This regular remainder solves an effective field equation which enjoys the benefit of having a non-singular source. Solving this effective field equation for the remainder completely avoids the calculation of the singular retarded field along with the attendant difficulties associated with numerically modeling a delta function source. From the differentiable remainder one may compute the self-force, the energy flux, and also a waveform which reflects the effects of the self-force. As a test of principle, we implement this method using a 4th-order (1+1) code, and calculate the self-force for the simple case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. We achieve agreement with frequency-domain results to 0.1% or better.- 04.25.Nx
- 04.25.D-
- 04.25.dg
- 04.20.Cv
- charge: scalar
- black hole: Schwarzschild
- energy: flux
- self-force
- charge: orbit
- regularization
References(32)
Figures(0)