Regular spherical dust spacetimes

TL;DR

This paper classifies all regular spherically symmetric dust spacetimes in general relativity, providing a comprehensive framework that unifies previous results and explores their topologies, junctions, and recollapse behavior.

Contribution

It offers a complete classification of regular dust spacetimes, including junction conditions and topological distinctions, extending and unifying earlier research.

Findings

Classified all regular spherically symmetric dust spacetimes.

Described junction conditions for non-comoving surfaces.

Identified four topological classes, including a 3-torus topology.

Abstract

Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction conditions are described for general non-comoving (and non-null) surfaces, and the limits of kinematical quantities are given on all comoving surfaces where there is Darmois matching. We show that an inhomogeneous generalisation of the Kantowski-Sachs metric may be joined to the Lemaitre-Tolman-Bondi metric. All the possible spacetimes are explicitly divided into four groups according to topology, including a group in which the spatial sections have the topology of a 3-torus. The recollapse conjecture (for these spacetimes) follows naturally in this approach.