Spacetime structure of self-similar spherically symmetric perfect fluid solutions

TL;DR

This paper classifies all spherically symmetric, self-similar solutions with perfect fluid matter, analyzing their spacetime structures and identifying those relevant as critical solutions in gravitational collapse.

Contribution

It provides a complete classification of homothetic spherically symmetric perfect fluid solutions and links them to critical phenomena in gravitational collapse.

Findings

Identified all possible kinematic structures for these solutions.

Mapped solutions to conformal diagrams for better understanding.

Highlighted solutions acting as critical points in collapse scenarios.

Abstract

We classify all spherically symmetric and homothetic spacetimes that are allowed kinematically by constructing them from a small number of building blocks. We then restrict attention to a particular dynamics, namely perfect fluid matter with the scale-free barotropic equation of state p = alpha mu where 0<alpha<1 is a constant. We assign conformal diagrams to all solutions in the complete classification of Carr and Coley, and so establish which of the kinematic possibilities are realized for these dynamics. We pay particular attention to those solutions which arise as critical solutions during gravitational collapse.