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# Advances in Theoretical and Mathematical Physics

## Volume 25 (2021)

### Number 2

### Static black holes in higher dimensional Einstein–Skyrme models

Pages: 507 – 541

DOI: https://dx.doi.org/10.4310/ATMP.2021.v25.n2.a5

#### Authors

#### Abstract

In this paper we construct a class of hairy static black holes of higher dimensional Einstein–Skyrme theories with the cosmological constant $\Lambda \leq 0$ 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 $N \geq 5$, 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.

Published 17 February 2022