Exact solutions for null fluid collapse

TL;DR

This paper derives exact spherically symmetric solutions to Einstein's equations for null fluids with pressure-density relations, revealing diverse horizon structures and black hole behaviors depending on parameters.

Contribution

It provides new exact solutions for null fluid collapse with pressure, extending known models and analyzing their horizon and asymptotic properties.

Findings

Metrics have multiple apparent horizons.

Asymptotically flat solutions are hairy black holes.

Solutions interpolate between Schwarzschild and Reissner-Nordstrom.

Abstract

Exact non-static spherically symmetric solutions of the Einstein equations for a null fluid source with pressure $P$ and density $\rho$ related by $P = k\rho^a$ are given. The $a=1$ metrics are asymptotically flat for $1/2<k\le 1$ and cosmological for $0<k<1/2$. The $k=1$ metric is the known charged Vaidya solution. In general the metrics have multiple apparent horizons. In the long time limit, the asymptotically flat metrics are hairy black hole solutions that `fall between' the Schwarzschild and Reissner-Nordstrom metrics.