Global Dynamics for the coupled Einstein-Maxwell system with pseudo-tensor of pressure on Bianchi spacetimes

TL;DR

This paper proves the global existence and analyzes the asymptotic behavior of solutions to the coupled Einstein-Maxwell system with a pseudo-tensor of pressure on Bianchi spacetimes, ensuring well-posedness and geodesic completeness.

Contribution

It establishes the global existence and well-posedness of the Einstein-Maxwell system with pressure pseudo-tensor on Bianchi I-VIII spacetimes, a novel extension in the field.

Findings

Proved global existence of solutions in Bianchi I-VIII spacetimes.

Analyzed geodesic completeness and asymptotic behavior.

Established positivity conditions for the system.

Abstract

Global existence to the coupled Einstein-Maxwell system which rules the dynamics of a kind of charged matter with a pseudo-tensor of pressure is proved, in Bianchi I-VIII spacetimes. We study the geodesics completeness, the asymptotic behavior, the positivity conditions, and we prove that the problem is well-posed in the sense of Hadamard.