  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.
