A classification (uniqueness) theorem for rotating black holes in 4D Einstein-Maxwell-dilaton theory

Abstract

In the present paper we prove a classification (uniqueness) theorem for stationary, asymptotically flat black hole spacetimes with connected and non-degenerate horizon in 4D Einstein-Maxwell-dilaton theory with an arbitrary dilaton coupling parameter $\alpha$. We show that such black holes are uniquely specified by the length of the horizon interval, angular momentum, electric and magnetic charge and the value of the dilaton field at infinity when the dilaton coupling parameter satisfies $0\le {\alpha }^2\le 3$. The proof is based on the nonpositivity of the Riemann curvature operator on the space of the potentials. A generalization of the classification theorem for spacetimes with disconnected horizons is also given.

15 pages, v2 typos corrected

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• Dynamical Collapse of Charged Scalar Field in Phantom Gravity
• A maximum magnetic moment to angular momentum conjecture
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• Collapse of Charged Scalar Field in Dilaton Gravity
• Area-angular momentum-charge inequality for stable marginally outer trapped surfaces in 4D Einstein-Maxwell-dilaton theory
• Dilatons and the Dynamical Collapse of Charged Scalar Field
• Electrically charged dilaton black holes in external magnetic field
• Thermodynamics of rotating charged dilaton black holes in an external magnetic field
• Nutty Kaluza-Klein dyons revisited
• From rotating attractors to extremal black holes with axionic hair