Rotating Dilaton Black Holes with Hair

TL;DR

This paper explores rotating black holes in SU(2) Einstein-Yang-Mills-dilaton theory, revealing new solutions with unique charge properties and a mass formula involving the dilaton charge, expanding understanding of non-Abelian black hole configurations.

Contribution

It introduces new rotating black hole solutions with non-trivial non-Abelian fields and a mass formula involving the dilaton charge, highlighting their unique charge characteristics and potential uniqueness.

Findings

Existence of rotating black holes with no non-Abelian charge due to the dilaton.

Sequences of solutions characterized by winding and node numbers.

A mass formula involving the dilaton charge instead of magnetic charge.

Abstract

We consider stationary rotating black holes in SU(2) Einstein-Yang-Mills theory, coupled to a dilaton. The black holes possess non-trivial non-Abelian electric and magnetic fields outside their regular event horizon. While generic solutions carry no non-Abelian magnetic charge, but non-Abelian electric charge, the presence of the dilaton field allows also for rotating solutions with no non-Abelian charge at all. As a consequence, these special solutions do not exhibit the generic asymptotic non-integer power fall-off of the non-Abelian gauge field functions. The rotating black hole solutions form sequences, characterized by the winding number $n$ and the node number $k$ of their gauge field functions, tending to embedded Abelian black holes. The stationary non-Abelian black hole solutions satisfy a mass formula, similar to the Smarr formula, where the dilaton charge enters instead of the magnetic charge. Introducing a topological charge, we conjecture, that black hole solutions in SU(2) Einstein-Yang-Mills-dilaton theory are uniquely characterized by their mass, their angular momentum, their dilaton charge, their non-Abelian electric charge, and their topological charge.