Matching Spherical Dust Solutions to Construct Cosmological Models

TL;DR

This paper develops methods for matching different spherically symmetric dust solutions to create consistent cosmological models, illustrating with a collapsing dust sphere that forms a black hole in a curved universe.

Contribution

It introduces a systematic approach for matching Lemaitre-Tolman-Bondi solutions to model inhomogeneous cosmologies with collapsing regions.

Findings

Singularity persists without vacuum regions, continuously accreting matter.

Method successfully models a collapsing dust sphere leading to black hole formation.

Provides conditions for smooth matching of different dust solutions.

Abstract

Conditions for smooth cosmological models are set out and applied to inhomogeneous spherically symmetric models constructed by matching together different Lemaitre-Tolman-Bondi solutions to the Einstein field equations. As an illustration the methods are applied to a collapsing dust sphere in a curved background. This describes a region which expands and then collapses to form a black hole in an Einstein de Sitter background. We show that in all such models if there is no vacuum region then the singularity must go on accreting matter for an infinite LTB time.