Static black holes in higher dimensional Einstein-Skyrme models

In this paper we construct a class of hairy static black holes of higher dimensional Einstein-Skyrme theories with the cosmolog-ical constant Lambda <= 0 whose scalar is an SU(2) valued field. The spacetime is set to be conformal to M-4 x NN-4 where M-4 and NN-4 are a four dimensional spacetime and a compact Einstein (N - 4)-dimensional submanifold for N >= 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 asymp-totic 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.

Automated summary

In this paper, a class of hairy static black holes in higher dimensional Einstein-Skyrme theories with a cosmological constant is constructed, considering a scalar field that is an SU(2) valued field. The study discusses the behavior of solutions near boundaries and establishes the local-global existence of black hole solutions, showing that black holes with finite energy exist under certain conditions. Additionally, linear stability analysis is performed to give insights into the stability of these black hole solutions.