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 ${\hat{I}}^3$: the Einstein-Maxwell coupling (${\hat{I}}^3=0$), corresponding to the Kerr-Newman (KN) solution, and the Kaluza-Klein coupling (${\hat{I}}^3=\sqrt{3}$). Rotating solutions with arbitrary ${\hat{I}}^3$ are known only in the slow-rotation or weakly charged limits. In this work, we numerically construct such EMd BHs with arbitrary ${\hat{I}}^3$. We present an overview of the parameter space of the solutions for illustrative values of ${\hat{I}}^3$ 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 $0<{\hat{I}}^3<\sqrt{3}$ possess a zero temperature limit, which, albeit regular in terms of curvature invariants, exhibits a $pp$-singularity. A different limiting behaviour is found for ${\hat{I}}^3>\sqrt{3}$, in which case, moreover, we have found hints of BH non-uniqueness for the same global charges.

38 pages, 16 figures. Published version

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