Regularization of fields for selfforce problems in curved spacetime: Foundations and a timedomain application
Abstract
We propose an approach for the calculation of selfforces, energy fluxes and waveforms arising from moving point charges in curved spacetimes. As opposed to modesum schemes that regularize the selfforce 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 selfforce is easily calculated. This regular remainder solves a wave equation which enjoys the benefit of having a nonsingular source. Solving this wave equation for the remainder completely avoids the calculation of the singular retarded field along with the attendant difficulties associated with numerically modeling a deltafunction source. From this differentiable remainder one may compute the selfforce, the energy flux, and also a waveform which reflects the effects of the selfforce. As a test of principle, we implement this method using a 4thorder (1+1) code, and calculate the selfforce for the simple case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. We achieve agreement with frequencydomain results to ∼0.1% or better.
 Publication:

Physical Review D
 Pub Date:
 April 2008
 DOI:
 10.1103/PhysRevD.77.084008
 arXiv:
 arXiv:0712.4405
 Bibcode:
 2008PhRvD..77h4008V
 Keywords:

 04.25.D;
 04.20.Cv;
 04.25.Nx;
 04.25.dg;
 Numerical relativity;
 Fundamental problems and general formalism;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Numerical studies of black holes and blackhole binaries;
 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, 12 figures, 1 table. More figures, extended summary