On the non-relativistic limit of the spherically symmetric Einstein-Vlasov-Maxwell system

TL;DR

This paper proves that solutions of the spherically symmetric Einstein-Vlasov-Maxwell system converge to solutions of the Vlasov-Poisson system as the speed of light tends to infinity, establishing a non-relativistic limit.

Contribution

It demonstrates the non-relativistic limit of the Einstein-Vlasov-Maxwell system under spherical symmetry, showing convergence to the Vlasov-Poisson system as c approaches infinity.

Findings

Solutions exist and are well-behaved for large c.

Solutions converge uniformly to the non-relativistic limit.

The strong energy condition holds for the relativistic system.

Abstract

The Einstein-Vlasov-Maxwell (EVM) system can be viewed as a relativistic generalization of the Vlasov-Poisson (VP) system. As it is proved below, one of nice property obeys by the first system is that the strong energy condition holds and this allows to conclude that the above system is physically viable. We show in this paper that in the context of spherical symmetry, solutions of the perturbed (EVM) system by $\gamma := 1/c^{2}$, $c$ being the speed of light, exist and converge uniformly in $L^{\infty}$-norm, as $c$ goes to infinity on compact time intervals to solutions of the non-relativistic (VP) system.