A leading approach to the modeling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic timelike geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes. © 2012 American Physical Society.
Publication Source (Journal or Book title)
Physical Review D - Particles, Fields, Gravitation and Cosmology
Wardell, B., Vega, I., Thornburg, J., & Diener, P. (2012). Generic effective source for scalar self-force calculations. Physical Review D - Particles, Fields, Gravitation and Cosmology, 85 (10) https://doi.org/10.1103/PhysRevD.85.104044