Exact flavored black $p$-branes and self-gravitating instantons from toroidal black holes with Skyrme hair

Abstract

In this paper, using the maximal embedding of $SU(2)$ into $SU(N)$ in the Euler angles parameterization, we construct a novel family of exact solutions of the Einstein $SU(N)$-Skyrme model. First, we present a hairy toroidal black hole in $D=4$ dimensions. This solution is asymptotically locally anti-de Sitter and is characterized by discrete hair parameters. Then, we perform a dimensional extension of the black hole to obtain black $p$-branes as solutions of the Einstein $SU(N)$-Non-linear sigma model in $D\ge 5$ dimensions. These are homogeneous and topologically protected. Finally we show that, through a Wick rotation of the toroidal black hole, one can construct an exact self-gravitating instanton. The role that the flavor number $N$ plays in the geometry and thermodynamics of these configurations is also discussed.

25 pages, 9 figures, some comments and references added, accepted for publication in Phys. Rev. D

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Cited by in corpus (1)

• Euclidean AdS wormholes and gravitational instantons in the Einstein-Skyrme theory