Uniqueness of (dilatonic) charged black holes and black p-branes in higher dimensions

TL;DR

This work establishes a higher-dimensional uniqueness theorem for static, electrically charged black holes with general vector-dilaton coupling, and extends the result to a broad class of black p-branes. The approach combines conformal transformations of the spatial metric with a higher-dimensional conformal positive energy theorem to deduce conformal flatness and spherical horizon geometry, recovering the higher-dimensional Reissner-Nordström and Gibbons-Maeda solutions. The non-extreme (nonzero surface gravity) assumption is essential to exclude multi-black-hole configurations. The results provide a robust rigidity statement for static black objects in theories motivated by string theory.

Abstract

We prove the uniqueness of higher dimensional (dilatonic) charged black holes in static and asymptotically flat spacetimes for arbitrary vector-dilaton coupling constant. An application to the uniqueness of a wide class of black p-branes is also given.