Prescriptions for numerical self-force calculations have traditionally been designed for frequency-domain or (1+1) time-domain codes which employ a mode decomposition to facilitate in carrying out a delicate regularization scheme. This has prevented self-force analyses from benefiting from the powerful suite of tools developed and used by numerical relativists for simulations of the evolution of comparable-mass black hole binaries. In this work, we revisit a previously-introduced (3+1) method for self-force calculations and demonstrate its viability by applying it to the test case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. Two (3+1) codes originally developed for numerical relativity applications were independently employed, and in each we were able to compute the two independent components of the self-force and the energy flux correctly to within <1%. We also demonstrate consistency between the t component of the self-force and the scalar energy flux. Our results constitute the first successful calculation of a self-force in a (3+1) framework, and thus open opportunities for the numerical relativity community in self-force analyses and the perturbative modeling of extreme-mass-ratio inspirals. © 2009 The American Physical Society.
Publication Source (Journal or Book title)
Physical Review D - Particles, Fields, Gravitation and Cosmology
Vega, I., Diener, P., Tichy, W., & Detweiler, S. (2009). Self-force with (3+1) codes: A primer for numerical relativists. Physical Review D - Particles, Fields, Gravitation and Cosmology, 80 (8) https://doi.org/10.1103/PhysRevD.80.084021