Gravitational Collapse: Expanding and Collapsing Regions

TL;DR

This paper develops a formalism using Israel junction conditions to analyze expanding and collapsing regions in spherically symmetric spacetimes, applying it to Minkowski and Kantowski-Sachs models.

Contribution

It introduces a general approach for studying dynamic regions in spacetime via junction conditions, specifically addressing expanding and collapsing shells.

Findings

Derived expressions for surface energy density and tangential pressure.

Identified conditions for minimal pressure to distinguish expanding and collapsing regions.

Applied formalism to Minkowski and Kantowski-Sachs spacetimes successfully.

Abstract

We investigate the expanding and collapsing regions by taking two well-known spherically symmetric spacetimes. For this purpose, the general formalism is developed by using Israel junction conditions for arbitrary spacetimes. This has been used to obtain the surface energy density and the tangential pressure. The minimal pressure provides the gateway to explore the expanding and collapsing regions. We take Minkowski and Kantowski-Sachs spacetimes and use the general formulation to investigate the expanding and collapsing regions of the shell.