Gravitationally Collapsing Shells in (2+1) Dimensions

TL;DR

This paper investigates various gravitational collapse scenarios of shells with different matter contents in (2+1)-dimensional spacetimes, revealing conditions for black hole formation, naked singularities, and diverse collapse behaviors.

Contribution

It provides a comprehensive analysis of collapse dynamics for dust, pressure fluids, and GCG shells in various (2+1)D backgrounds, including conditions for different end states.

Findings

Collapse of dust shells can lead to black holes with high initial density.

Naked singularities can form under broad initial conditions.

GCG shells show diverse collapse outcomes analyzed via effective potential.

Abstract

We study gravitationally collapsing models of pressureless dust, fluids with pressure, and the generalized Chaplygin gas (GCG) shell in (2+1)-dimensional spacetimes. Various collapse scenarios are investigated under a variety of the background configurations such as anti-de Sitter(AdS) black hole, de Sitter (dS) space, flat and AdS space with a conical deficit. As with the case of a disk of dust, we find that the collapse of a dust shell coincides with the Oppenheimer-Snyder type collapse to a black hole provided the initial density is sufficiently large. We also find -- for all types of shell -- that collapse to a naked singularity is possible under a broad variety of initial conditions. For shells with pressure this singularity can occur for a finite radius of the shell. We also find that GCG shells exhibit diverse collapse scenarios, which can be easily demonstrated by an effective potential analysis.