Static Black Holes in Higher Dimensional Einstein-Skyrme Models

TL;DR

This paper constructs and analyzes static black hole solutions in higher-dimensional Einstein-Skyrme theories with a scalar field, exploring their existence, boundary behavior, and stability properties.

Contribution

It introduces a class of higher-dimensional hairy black holes with scalar hair, establishing their existence and stability characteristics.

Findings

Black hole solutions exist with finite energy in asymptotically Ricci-flat geometries.

Solutions are constructed near horizons and at infinity, showing boundary behaviors.

Linear stability analysis suggests certain solutions are stable.

Abstract

In this paper we construct a class of hairy static black holes of higher dimensional Einstein-Skyrme theories with the cosmological constant $\Lambda \le 0$ whose scalar is an $SU(2)$ valued field. The spacetime is set to be conformal to $ \mathcal{M}^4 \times \mathcal{N}^{N-4}$ where $\mathcal{M}^4$ and $\mathcal{N}^{N-4}$ are a four dimensional spacetime and a compact Einstein $(N-4)$-dimensional submanifold for $N \ge 5$, respectively, whereas $N=4$ is the trivial case. We discuss the behavior of solutions near the boundaries, namely, near the (event) horizon and in the asymptotic region. Then, we establish local-global existence of black hole solutions and show that black holes with finite energy exist if their geometries are asymptotically Ricci-flat. At the end, we perform a linear stability analysis using perturbative method and give a remark about their stability.