Gravitational Collapse of Inhomogeneous Dust in (2+1) Dimensions

TL;DR

This paper analyzes the gravitational collapse of inhomogeneous dust in (2+1) dimensions with a cosmological constant, deriving solutions, matching exterior metrics, and studying singularity and trapped surface formation.

Contribution

It provides analytical solutions for inhomogeneous dust collapse in (2+1) dimensions and explores the nature of resulting singularities and trapped surfaces.

Findings

Singularities can form during collapse under certain conditions.

Trapped surfaces may or may not form depending on initial data.

The nature of the singularity is influenced by inhomogeneity and cosmological constant.

Abstract

We examine the gravitational collapse of spherically symmetric inhomogeneous dust in (2+1) dimensions, with cosmological constant. We obtain the analytical expressions for the interior metric. We match the solution to a vacuum exterior. We discuss the nature of the singularity formed by analyzing the outgoing radial null geodesics. We examine the formation of trapped surfaces during the collapse.