Exact Einstein-scalar field solutions for formation of black holes in a cosmological setting

TL;DR

This paper presents exact solutions to Einstein's equations involving scalar fields, demonstrating black hole formation in a cosmological context with different horizon types and discussing implications for cosmic censorship.

Contribution

It introduces two classes of exact Einstein-scalar solutions, including a novel solution modeling black hole formation in a cosmological setting with critical behavior.

Findings

Existence of solutions with both black hole and cosmological horizons

Identification of a critical parameter affecting horizon structure

Presence of a mild curvature singularity affecting extended bodies

Abstract

We consider self-interacting scalar fields coupled to gravity. Two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling. One of the solutions is shown to describe a formation of a black hole in a cosmological setting. Some properties of this solution are described. There are two kinds of event horizons: a black hole horizon and cosmological horizons. The cosmological horizons are not smooth. There is a mild curvature singularity, which affects extended bodies but allows geodesics to be extended. It is also shown that there is a critical value for a parameter on which the solution depends. Above the critical point, the black hole singularity is hidden within a global black hole event horizon. Below the critical point, the singularity appears to be naked. The relevance to cosmic censorship is discussed.