Matching of spatially homogeneous non-stationary space--times to vacuum in cylindrical symmetry

TL;DR

This paper investigates the mathematical matching of collapsing dust space-times with non-stationary vacuum exteriors under cylindrical symmetry, revealing complex features like trapped surfaces, singularities, and horizons.

Contribution

It provides existence and uniqueness results for the exterior solutions and analyzes their geometric and singularity properties.

Findings

Matched solutions contain trapped surfaces and singularities.

Solutions include Cauchy horizons with evidence of singularity.

Solutions are not asymptotically flat.

Abstract

We study the matching of LRS spatially homogeneous collapsing dust space-times with non-stationary vacuum exteriors in cylindrical symmetry. Given an interior with diagonal metric we prove existence and uniqueness results for the exterior. The matched solutions contain trapped surfaces, singularities and Cauchy horizons. The solutions cannot be asymptotically flat and we present evidence that they are singular on the Cauchy horizons.