Uniqueness theorem for static dilaton U(1)^2 black holes

TL;DR

This paper proves a uniqueness theorem for static dilaton U(1)^2 black holes in N=4, d=4 supergravity, employing a sigma model approach on a two-dimensional manifold, and considers solutions in different gauge groups.

Contribution

It provides the first rigorous proof of black hole uniqueness in this supergravity context using a sigma model formulation.

Findings

Uniqueness of static dilaton U(1)^2 black holes established

Proof applies to both SU(4) and SO(4) gauge groups

Method employs a sigma model on a two-dimensional manifold

Abstract

Using a sigma model formulation of the field equations as on a two-dimensional manifold we provide the proof of a black hole uniqueness solution in N=4, d=4 supergravity subject to certain boundary conditions. We considered the black hole solutions both in SU(4) and SO(4) versions of the underlying theory.