Numerical evaluation of the self-force on a point particle is made difficult by the use of delta functions as sources. Recent methods for self-force calculations avoid delta functions altogether, using instead a finite and extended 'effective source' for a point particle. We provide a review of the general principles underlying this strategy, using the specific example of a scalar point charge moving in a black hole spacetime. We also report on two new developments: (i) the construction and evaluation of an effective source for a scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii) the successful implementation of hyperboloidal slicing that significantly improves on previous treatments of boundary conditions used for effective-source-based self-force calculations. Finally, we identify some of the key issues related to the effective source approach that will need to be addressed by future work. © 2011 IOP Publishing Ltd.
Publication Source (Journal or Book title)
Classical and Quantum Gravity
Vega, I., Wardell, B., & Diener, P. (2011). Effective source approach to self-force calculations. Classical and Quantum Gravity, 28 (13) https://doi.org/10.1088/0264-9381/28/13/134010