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

Bobby E. Gunara (Indonesian Center for Theoretical and Mathematical Physics (ICTMP) and Theoretical Physics Laboratory, Theoretical High Energy Physics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)

Fiki T. Akbar (Theoretical Physics Laboratory, Theoretical High Energy Physics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)

Rizqi Fadli (Theoretical Physics Laboratory, Theoretical High Energy Physics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)

Deden M. Akbar (Theoretical Physics Laboratory, Theoretical High Energy Physics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)

Hadi Susanto (Theoretical Physics Laboratory, Theoretical High Energy Physics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia; and Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom)

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.

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Published 17 February 2022