Gravitational Collapse of Self-Similar Perfect Fluid in 2+1 Gravity

TL;DR

This paper explores gravitational collapse in 2+1 dimensional spacetimes with perfect fluids exhibiting self-similarity, providing exact solutions and analyzing their implications for black hole and naked singularity formation.

Contribution

It presents a comprehensive set of exact solutions for self-similar perfect fluids in 2+1 gravity, including cases of dust, stiff fluids, and linear equations of state, and studies their collapse outcomes.

Findings

Some solutions lead to black hole formation.

Others result in naked singularities.

The final state depends on initial conditions and fluid properties.

Abstract

Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. In particular, these include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind, and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth or second kind. It is found that some of these solutions represent gravitational collapse, and the final state of the collapse can be either black holes or naked singularities.