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

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<mark>Journal publication date</mark>5/11/2010
<mark>Journal</mark>Journal of Physics A: Mathematical and Theoretical
Issue number44
Pages (from-to)445502
Publication StatusPublished
<mark>Original language</mark>English


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.