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

TL;DR

This paper proves a uniqueness theorem for stationary black holes in 4D Einstein-Maxwell-dilaton theory, showing they are characterized by specific parameters when the dilaton coupling is within a certain range.

Contribution

It establishes a classification theorem for black holes with connected horizons in Einstein-Maxwell-dilaton theory for arbitrary dilaton coupling within a specified range.

Findings

Black holes are uniquely determined by horizon length, angular momentum, charges, and dilaton value at infinity.

The proof uses the nonpositivity of the Riemann curvature operator on potential space.

A generalization for spacetimes with disconnected horizons is provided.

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 $0\le \alpha^2\le3$. 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.