2014/04/28 by Thomas M. Linz, John L. Friedman, Alan G. Wiseman +1 · 6 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Classical mechanics #Experimental and Theoretical Physics Studies #General relativity #Geodesic #Gravitation #Mathematical analysis #Mathematical physics #Mathematics #Physics #Point particle #Pulsars and Gravitational Waves Research #Quantum mechanics #Regularization (linguistics) #Renormalization #Scalar field #Schwarzschild metric #Schwarzschild radius #Spacetime #gr-qc
paper · pdf · doi:10.1103/physrevd.90.024064
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 90(2) (American Physical Society) · 54 pages, 1 figure
arxiv created 2014/04/28 · openalex publication_date 2014/07/23 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We calculate the singular field of an accelerated point particle (scalar charge, electric charge or small gravitating mass) moving on an accelerated (nongeodesic) trajectory in a generic background spacetime. Using a mode-sum regularization scheme, we obtain explicit expressions for the self-force regularization parameters. We use a Lorentz gauge for the electromangetic and gravitational cases. This work extends the work of Barack and Ori [1] who demonstrated that the regularization parameters for a point particle in geodesic motion in a Schwarzschild spacetime can be described solely by the leading and subleading terms in the mode-sum (commonly known as the A and B terms) and that all terms of higher order in \ensuremathℓ vanish upon summation (later they showed the same behavior for geodesic motion in Kerr [2], [3]). We demonstrate that these properties are universal to point particles moving through any smooth spacetime along arbitrary (accelerated) trajectories. Our renormalization scheme is based on, but not identical to, the Quinn-Wald axioms. As we develop our approach, we review and extend work showing that that different definitions of the singular field used in the literature are equivalent to our approach. Because our approach does not assume geodesic motion of the perturbing particle, we are able use our mode-sum formalism to explicitly recover a well-known result: The self-force on static scalar charges near a Schwarzschild black hole vanishes.