Generalized Skyrmions and hairy black holes in asymptotically AdS$_4$ spacetime

TL;DR

This paper studies black hole solutions with Skyrmion fields in four-dimensional anti-de Sitter space, analyzing how the cosmological constant and gravitational coupling influence their properties, confirming the necessity of the Skyrme term for hairy black holes.

Contribution

It extends the Einstein-Skyrme model to asymptotically AdS space, exploring the effects of cosmological constant and gravitational coupling on black hole solutions with Skyrmionic hair.

Findings

Increasing the cosmological constant mimics increasing gravitational coupling.

Skyrme term is essential for black holes with Skyrmionic hair.

Black hole solutions depend on the interplay of cosmological constant and coupling strength.

Abstract

We investigate the properties of spherically symmetric black hole solutions in the generalized Einstein-Skyrme model theory in four-dimensional asymptotically anti-de Sitter space-time. The dependencies of the Skyrmion fields on the cosmological constant and on the strength of the effective gravitational coupling are examined. We show that the increase of the absolute value of the cosmological constant qualitatively yields the same effect as increasing of the effective gravitational coupling. We confirm that, similar to the model in the asymptotically flat space-time, a necessary condition for the existence of black holes with Skyrmionic hair is the inclusion of the Skyrme term.