Rotating dilaton black holes with hair
Abstract
We consider stationary rotating black holes in SU(2) Einstein-Yang-Mills theory, coupled to a dilaton. The black holes possess nontrivial 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 noninteger power falloff 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.