Uniqueness and nonuniqueness of the stationary black holes in 5D Einstein-Maxwell and Einstein-Maxwell-dilaton gravity

TL;DR

This paper investigates the uniqueness and nonuniqueness of stationary black hole solutions in five-dimensional Einstein-Maxwell and Einstein-Maxwell-dilaton gravity, providing classification theorems based on physical charges and geometric structures.

Contribution

It formulates and proves new uniqueness theorems for 5D black holes, incorporating arbitrary dilaton coupling and classifying solutions via interval structure and charges.

Findings

Uniqueness theorems for certain black hole solutions

Classification based on interval structure and charges

Restrictions on dilaton coupling parameters

Abstract

In the present paper we investigate the general problem of uniqueness of the stationary black solutions in 5D Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling parameter containing the Einstein-Maxwell gravity as a particular case. We formulate and prove uniqueness theorems classifying the stationary black hole solutions in terms of their interval structure, electric and magnetic charges and the magnetic fluxes. The proofs are based on the nonpositivity of the Riemann curvature operator on the space of the potentials which imposes restrictions on the dilaton coupling parameter.