Gravitational collapse of spherically symmetric perfect fluid with kinematic self-similarity

TL;DR

This paper analyzes exact spherically symmetric solutions of Einstein's equations with perfect fluids exhibiting self-similarity, exploring their roles in gravitational collapse and black hole formation, including critical phenomena and specific solution cases.

Contribution

It identifies and studies self-similar solutions of various kinds, revealing their relevance to gravitational collapse and critical phenomena, and relates known solutions to these classes.

Findings

Some solutions represent gravitational collapse leading to black holes.

Certain solutions act as critical solutions separating black hole and naked singularity formation.

De Sitter and Schwarzschild solutions are special cases within these self-similar classes.

Abstract

Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav. {\bf 15}, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The formation of such black holes always starts with a mass gap, although the "critical" solution has homothetic self-similarity. The solutions with self-similarity of the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is also found that the de Sitter solution is a particular case of the solutions with self-similarity of the zeroth kind, and that the Schwarzschild solution is a particular case of the solutions with self-similarity of the second kind with the index $\alpha = 3/2$.