Black hole solutions in 2+1 dimensions

TL;DR

This paper derives circularly symmetric solutions for null fluid collapse in 2+1-dimensional Einstein gravity with a cosmological constant, revealing different black hole structures depending on the fluid's pressure-density relation.

Contribution

It provides new exact solutions describing null fluid collapse in 2+1 dimensions, connecting fluid properties to black hole horizon structures.

Findings

For k=1, solutions reduce to BTZ black holes.

For k<1, solutions describe hairy black holes.

Long-term solutions depend on the pressure-density relation.

Abstract

We give circularly symmetric solutions for null fluid collapse in 2+1-dimensional Einstein gravity with a cosmological constant. The fluid pressure $P$ and energy density $\rho$ are related by $P=k\rho$ $(k\le 1)$. The long time limit of the solutions are black holes whose horizon structures depend on the value of $k$. The $k=1$ solution is the Banados-Teitelboim-Zanelli black hole metric in the long time static limit, while the $k<1$ solutions give other, `hairy' black hole metrics in this limit.