Axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime

1996/10/24 by Theodore C. Quinn, Robert M. Wald · 511 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Electromagnetic field #Experimental and Theoretical Physics Studies #Geodesic #Gravitation #Gravitational field #Mathematical analysis #Mathematics #Motion (physics) #Physics #Point particle #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Relativity and Gravitational Theory #Spacetime #gr-qc

paper · pdf · doi:10.1103/physrevd.56.3381

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 56(6), 3381-3394 (American Physical Society) · 37 pages, LaTeX with style package RevTeX 3.0

arxiv created 1996/10/24 · openalex publication_date 1997/09/15 · arxiv updated 2011/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The problem of determining the electromagnetic and gravitational ``self-force'' on a particle in a curved spacetime is investigated using an axiomatic approach. In the electromagnetic case, our key postulate is a ``comparison axiom,'' which states that whenever two particles of the same charge e have the same magnitude of acceleration, the difference in their self-force is given by the ordinary Lorentz force of the difference in their (suitably compared) electromagnetic fields. We thereby derive an expression for the electromagnetic self-force which agrees with that of DeWitt and Brehme as corrected by Hobbs. Despite several important differences, our analysis of the gravitational self-force proceeds in close parallel with the electromagnetic case. In the gravitational case, our final expression for the (reduced order) equations of motion shows that the deviation from geodesic motion arises entirely from a ``tail term,'' in agreement with recent results of Mino et al. Throughout the paper, we take the view that ``point particles'' do not make sense as fundamental objects, but that ``point particle equations of motion'' do make sense as means of encoding information about the motion of an extended body in the limit where not only the size but also the charge and mass of the body go to zero at a suitable rate. Plausibility arguments for the validity of our comparison axiom are given by considering the limiting behavior of the self-force on extended bodies.

Citations

• Spinors and Space-Time
• Classical Electrodynamics

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