Dynamics of a planar thin shell at a Taub-FRW junction

TL;DR

This paper explores the junction of Taub and FRW spacetimes using the Israel thin-shell formalism, providing insights into planar singularity formation and enhancing understanding of planar-symmetric systems in general relativity.

Contribution

It introduces a method to join vacuum Taub and flat FRW spacetimes, offering a new perspective on planar singularity formation in Einstein's theory.

Findings

A mechanism for planar singularity formation is proposed.

The junction modeling enhances understanding of planar-symmetric systems.

Insights into the dynamics of thin shells in general relativity are provided.

Abstract

We address the problem of stitching together the vacuum, static, planar-symmetric Taub spacetime and the flat Friedmann-Robertson-Walker cosmology using the Israel thin-shell formalism. The joining of Taub and FRW spacetimes is reminiscent of the Oppenheimer-Snyder collapse used in modeling the formation of a singularity from a collapsing spherical ball of dust. A possible mechanism for the formation of a planar singularity is provided. It is hoped that tackling such example will improve our intuition on planar-symmetric systems in Einstein's general relativity.