Perlick, Volker and Carr, Anthony (2010) On the initial-value problem of the Maxwell-Lorentz equations. Journal of Physics A: Mathematical and Theoretical, 43 (44). p. 445502. ISSN 1751-8113
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.