Charged, rotating black holes in Einstein-Maxwell-dilaton theory

Abstract

The asymptotically flat, electrically charged, rotating black holes (BHs) in Einstein-Maxwell-dilaton (EMd) theory are known in closed form for \textit{only} two particular values of the dilaton coupling constant $γ$: the Einstein-Maxwell coupling ($γ=0$), corresponding to the Kerr-Newman (KN) solution, and the Kaluza-Klein coupling ($γ=\sqrt{3}$). Rotating solutions with arbitrary $γ$ are known only in the slow-rotation or weakly charged limits. In this work, we numerically construct such EMd BHs with arbitrary $γ$. We present an overview of the parameter space of the solutions for illustrative values of $γ$ together with a study of their basic properties. The solutions are in general KN-like; there are however, new features. The data suggest that the spinning solutions with $0<γ<\sqrt{3}$ possess a zero temperature limit, which, albeit regular in terms of curvature invariants, exhibits a $pp$-singularity. A different limiting behaviour is found for $γ>\sqrt{3}$, in which case, moreover, we have found hints of BH non-uniqueness for the same global charges.