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

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

2010-07-06

arxiv.org/abs/1007.0953v2

J.Phys.A43:445502,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 3 figures. One reference added. To appear in J. Phys. A

Scientific paper

10.1088/1751-8113/43/44/445502

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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