2012/06/17 by Marc Casals, Eric Poisson, Ian Vega · 3 citations
Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Black Holes and Theoretical Physics #Classical mechanics #Computation #Computer science #Conjecture #Cosmology and Gravitation Theories #Dimensional regularization #Hadamard transform #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Regularization (linguistics) #Renormalization #Spacetime #gr-qc
paper · pdf · doi:10.1103/physrevd.86.064033
23 pages, no figures
arxiv created 2012/06/17 · openalex publication_date 2012/09/18 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Various regularization methods have been used to compute the self-force acting on a static particle in a static, curved spacetime. Many of these are based on Hadamard's two-point function in three dimensions. On the other hand, the regularization method that enjoys the best justification is that of Detweiler and Whiting, which is based on a four-dimensional Green's function. We establish the connection between these methods and find that they are all equivalent, in the sense that they all lead to the same static self-force. For general static spacetimes, we compute local expansions of the Green's functions on which the various regularization methods are based. We find that these agree up to a certain high order, and conjecture that they might be equal to all orders. We show that this equivalence is exact in the case of ultrastatic spacetimes. Finally, our computations are exploited to provide regularization parameters for a static particle in a general static and spherically symmetric spacetime.