On the initial-value problem of the Maxwell–Lorentz equations

DOI10.1088/1751-8113/43/44/445502zbMATH Open1205.78002arXiv1007.0953OpenAlexW3106364662WikidataQ62005850 ScholiaQ62005850MaRDI QIDQ3060124

Anthony Carr, Volker Perlick

Publication date: 1 December 2010

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell's equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and we demonstrate that the evolution equations are strongly hyperbolic. This result guarantees that the initial-value problem of the Maxwell-Lorentz equations is well-posed. We illustrate this general result with a discussion of spherically symmetric solutions on Minkowski spacetime.

Full work available at URL: https://arxiv.org/abs/1007.0953

zbMATH Keywords

Minkowski spacetimespherically symmetric solutionsMaxwell-Lorentz equationsgeneral-relativistic spacetime

Mathematics Subject Classification ID

Electromagnetic theory (general) (78A25) Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory (78-02)

Related Items (3)

The Lavrentiev-Ishlinsky problem at the initial stage of motion ⋮ The Goursat problem for Maxwell’s equations ⋮ On Exact Solutions of the Lorentz-Maxwell Equations

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