Plane Symmetric Gravitational Collapse

TL;DR

This paper develops a general framework for analyzing plane symmetric gravitational collapse using Israel's method, applying it to specific spacetimes to determine conditions for collapse or expansion.

Contribution

It introduces a new formulation for plane symmetric collapse and applies it to known metrics, providing insights into collapse and expansion scenarios.

Findings

Plane can collapse under certain conditions.

Plane can also expand depending on parameters.

The formulation applies to static and non-static plane symmetric spacetimes.

Abstract

In this paper, we derive the general formulation by considering two arbitrary plane symmetric spacetimes using Israel's method. As an example, we apply this formulation to known plane symmetric spacetimes. We take the Taub's static metric in the interior region whereas Kasner's non-static metric in the exterior region. It is shown that the plane collapses in some cases whereas it expands in some other cases.