Critical phenomena and a new class of self-similar spherically symmetric perfect-fluid solutions

TL;DR

This paper investigates self-similar solutions in gravitational collapse of perfect fluids, revealing a new class of asymptotically Minkowski spacetimes for certain equations of state, and explores their implications for critical phenomena.

Contribution

It identifies the global structure of self-similar solutions in perfect-fluid collapse and introduces a new class of solutions for specific values of the equation of state parameter.

Findings

Critical solutions are sensitive to the equation of state parameter α.

A new class of asymptotically Minkowski self-similar spacetimes is identified for α>0.28.

Implications for understanding critical phenomena in gravitational collapse.

Abstract

We consider the self-similar solutions associated with the critical behavior observed in the gravitational collapse of spherically symmetric perfect fluids with equation of state $p=\alpha\mu$. We identify for the first time the global nature of these solutions and show that it is sensitive to the value of $\alpha$. In particular, for $\alpha>0.28$, we show that the critical solution is associated with a new class of asymptotically Minkowski self-similar spacetimes. We discuss some of the implications of this for critical phenomena.