The Einstein-Vlasov-Maxwell(EVM) System with Spherical Symmetry

TL;DR

This paper investigates the global existence of solutions to the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data, showing singularities, if they occur, originate at the center of symmetry.

Contribution

It provides a proof of global solutions for small initial data and characterizes the potential singularity formation point in the EVM system.

Findings

Global in time solutions exist for small initial data.

Singularities, if they develop, occur at the center of symmetry.

The analysis applies to asymptotically flat, spherically symmetric configurations.

Abstract

We look for the global in time solution of the Cauchy problem corresponding to the asymptotically flat spherically symmetric EVM system with small initial data. Using an estimate, we also prove that if solution of the system stated above develops a singularity at all time, then the first one has to appear at the center of symmetry.