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

TL;DR

This paper numerically constructs and analyzes charged, rotating black holes in Einstein-Maxwell-dilaton theory for arbitrary dilaton coupling, revealing new features and potential non-uniqueness in their solutions.

Contribution

It provides the first numerical solutions for rotating black holes with arbitrary dilaton coupling, extending beyond known special cases and exploring their properties.

Findings

Solutions are generally Kerr-Newman-like but with new features.

Spinning solutions with $0<b3<\u0003b3_{KK}$ have a zero temperature limit with a $pp$-singularity.

Hints of black hole non-uniqueness for the same global charges when b3>b3_{KK}.

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