## Abstract

In this paper we construct a class of hairy static black holes of higher dimensional Einstein-Skyrme theories with the cosmological constant Λ ≤ 0 whose scalar is an SU(2) valued field. The spacetime is set to be conformal to M^{4} × N^{N−4} where M^{4} and N^{N−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 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.

Original language | British English |
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Pages (from-to) | 507-541 |

Number of pages | 35 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 25 |

Issue number | 2 |

DOIs | |

State | Published - 2021 |