Generating dynamical black hole solutions

TL;DR

This paper proves a theorem characterizing a broad family of non-static, spherically symmetric solutions to Einstein's equations, encompassing known dynamical black hole solutions and extending previous static solutions.

Contribution

It introduces a general theorem that describes a large family of non-static black hole solutions, extending prior work to dynamic cases and including static solutions for Type I fluid.

Findings

Identifies a large family of non-static solutions to Einstein equations.

Shows that known dynamical black hole solutions are special cases of this family.

Retrieves static black hole solutions for Type I fluid.

Abstract

We prove a theorem that characterizes a large family of non-static solutions to Einstein equations, representing, in general, spherically symmetric Type II fluid. It is shown that the best known dynamical black hole solutions to Einstein equations are particular cases from this family. Thus we extend a recent work of Salgado \cite{ms} to non-static case. The spherically symmetric static black hole solutions, for Type I fluid, are also retrieved.