On surface-symmetric spacetimes with collisionless and charged matter

TL;DR

This paper investigates the global behavior of cosmological solutions in Einstein-Vlasov-Maxwell systems with surface symmetry, proving global existence and completeness, and analyzing decay properties for inhomogeneous solutions.

Contribution

It establishes global existence and completeness results for symmetric Einstein-Vlasov-Maxwell solutions, including inhomogeneous cases with small initial data, and explores decay properties.

Findings

Homogeneous spacetimes are future complete for causal trajectories.

Inhomogeneous plane-symmetric solutions with small initial data are future complete.

Decay properties are established at late times for certain solutions.

Abstract

Some future global properties of cosmological solutions for the Einstein-Vlasov-Maxwell system with surface symmetry are presented. Global existence is proved, the homogeneous spacetimes are future complete for causal trajectories, and the same is true for inhomogeneous plane-symmetric solutions with small initial data. In the latter case some decay properties are also obtained at late times. Similar but slightly weaker results hold for hyperbolic symmetry.