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This paper is concerned with the asymptotic behavior of small data solutionsto the three-dimensional Vlasov-Maxwell system in the exterior of a light cone.The plasma does not have to be neutral and no compact support assumptions arerequired on the data. In particular, the initial decay in the velocity variableof the particle density is optimal and we only require an $L^2$ bound on theelectromagnetic field with no additional weight. We use vector field methods toderive improved decay estimates in null directions for the electromagneticfield, the particle density and their derivatives. In contrast with\cite{dim3}, where we studied the behavior of the solutions in the wholespacetime, the initial data have less decay and we do not need to modify thecommutation vector fields of the relativistic transport operator. To controlthe solutions under these assumptions, we crucially use the strong decaysatisfied by the particle density in the exterior of the light cone, nullproperties of the Vlasov equation and certain hierarchies in the energy norms.

Asymptotic properties of the solutions to the Vlasov-Maxwell system in the exterior of a light cone