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We propose an approach for the calculation of self-forces, energy fluxes andwaveforms arising from moving point charges in curved spacetimes. As opposed tomode-sum schemes that regularize the self-force derived from the singularretarded field, this approach regularizes the retarded field itself. Thesingular part of the retarded field is first analytically identified andremoved, yielding a finite, differentiable remainder from which the self-forceis easily calculated. This regular remainder solves a wave equation whichenjoys the benefit of having a non-singular source. Solving this wave equationfor the remainder completely avoids the calculation of the singular retardedfield along with the attendant difficulties associated with numericallymodeling a delta function source. From this differentiable remainder one maycompute the self-force, the energy flux, and also a waveform which reflects theeffects of the self-force. As a test of principle, we implement this methodusing a 4th-order (1+1) code, and calculate the self-force for the simple caseof a scalar charge moving in a circular orbit around a Schwarzschild blackhole. We achieve agreement with frequency-domain results to ~ 0.1% or better.

Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application