Black hole and BTZ-black string in the Einstein-SU(2) Skyrme model

TL;DR

This paper introduces new analytic black hole and black string solutions in the Einstein-SU(2) Skyrme model with negative cosmological constant, revealing complex thermodynamics and phase structures.

Contribution

It provides the first analytic hairy black hole solutions with flat base manifolds and constructs black strings with BTZ black hole geometry in this context.

Findings

Rich phase diagram with multiple thermodynamic phases

Existence of hairy black hole solutions with flat base manifolds

Black strings characterized by BTZ black hole geometry

Abstract

We present novel analytic hairy black holes with a flat base manifold in the (3+1)-dimensional Einstein SU(2)-Skyrme system with negative cosmological constant. We also construct (3+1)-dimensional black strings in the Einstein $SU(2)$-non linear sigma model theory with negative cosmological constant. The geometry of these black strings is a three-dimensional charged BTZ black hole times a line, without any warp factor. The thermodynamics of these configurations (and its dependence on the discrete hairy parameter) is analyzed in details. A very rich phase diagram emerges.