The Constraint Equations of the Einstein-Vlasov-Maxwell System in the Maximal-isotropic Coordinates

Abstract

In this paper we prove the existence of initial data satisfying the constraint equations corresponding to the 1+3 formulation of asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system, when the charge of the particles is either low or large, the initial distribution function is compactly supported, the shift vector is non-zero and the isotropic metric ansatz is not diagonal. This result extends the work (Rein and Rendall, Commun. Math. Phys. 150(3), 561–583 1992) concerning the existence of solutions to the constraint equations for chargeless particles.