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arXiv · 2303.17442

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

Patrick Concha·Carla Henríquez-Baez·Evelyn Rodríguez·Aldo Vera
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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 $D\geq5$ 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.

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Patrick Concha, Carla Henríquez-Baez, Evelyn Rodríguez, Aldo Vera. 2023-03-30. Exact flavored black $p$-branes and self-gravitating instantons from toroidal black holes with Skyrme hair. https://doi.org/10.1103/physrevd.107.124043

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