On future geodesic completeness for the Einstein-Vlasov system with hyperbolic symmetry

TL;DR

This paper proves that certain spacetimes with collisionless matter and hyperbolic symmetry are complete in the expanding direction, under specific initial data restrictions, ensuring no geodesic incompleteness occurs.

Contribution

It establishes future geodesic completeness for Einstein-Vlasov spacetimes with hyperbolic symmetry under size restrictions on initial data.

Findings

Spacetimes are timelike and null geodesically complete in the expanding direction.

Completeness holds for data satisfying a particular size restriction.

Results apply to collisionless matter evolving from compact Cauchy surfaces.

Abstract

Spacetimes with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry are shown to be timelike and null geodesically complete in the expanding direction, provided the data satisfy a certain size restriction.