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arXiv · 1007.0953

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

Volker Perlick·Anthony Carr
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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.

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Volker Perlick, Anthony Carr. 2010-07-06. On the initial-value problem of the Maxwell-Lorentz equations. https://doi.org/10.1088/1751-8113/43/44/445502

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