Gravitational Collapse of Circularly Symmetric Stiff Fluid with Self-Similarity in 2+1 Gravity

TL;DR

This paper analyzes the stability of self-similar stiff fluid solutions with circular symmetry in 2+1 gravity, finding most are unstable and none serve as critical solutions.

Contribution

It provides a stability analysis of homothetic self-similar solutions in 2+1 gravity, identifying which are unstable and not critical.

Findings

Most solutions have multiple unstable modes

Solutions with n=1 and n=3 are exceptions but still unstable

None of the solutions are critical in gravitational collapse

Abstract

Linear perturbations of homothetic self-similar stiff fluid solutions, $S[n]$, with circular symmetry in 2+1 gravity are studied. It is found that, except for those with $n = 1$ and $n = 3$, none of them is stable and all have more than one unstable mode. Hence, {\em none of these solutions can be critical}.