Local Existence and Continuation Criterion for Solutions of the Spherically Symmetric Einstein-Vlasov-Maxwell System

TL;DR

This paper establishes local existence, uniqueness, and a continuation criterion for global solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data using an iterative scheme.

Contribution

It introduces a new iterative approach to prove local existence and a continuation criterion for global solutions in this coupled system.

Findings

Proved local existence and uniqueness of solutions.

Established a continuation criterion for global solutions.

Demonstrated the effectiveness of the iterative scheme.

Abstract

Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.