Cylindrically symmetric inhomogeneous dust collapse with a zero expansion component

TL;DR

This paper presents new exact solutions for cylindrically symmetric inhomogeneous dust spacetimes with a zero expansion component, analyzing their properties, uniqueness, and physical implications such as trapped surfaces and gravitational radiation.

Contribution

It introduces novel solutions for Einstein's equations with a cosmological constant and demonstrates their uniqueness within the specified class.

Findings

New exact solutions for $mbda$-dust spacetimes with zero expansion.

Recovery of the Senovilla-Vera metric for zero cosmological constant.

Analysis of trapped surfaces and gravitational radiation in the exterior region.

Abstract

We investigate a class of cylindrically symmetric inhomogeneous $\Lambda$-dust spacetimes which have a regular axis and some zero expansion component. For $\Lambda\ne 0$, we obtain new exact solutions to the Einstein equations and show that they are unique, within that class. For $\Lambda=0$, we recover the Senovilla-Vera metric and show that it can be locally matched to an Einstein-Rosen type of exterior. Finally, we explore some consequences of the matching, such as trapped surface formation and gravitational radiation in the exterior.