On uniqueness of static Einstein-Maxwell-dilaton black holes

TL;DR

This paper proves the uniqueness of static, asymptotically flat Einstein-Maxwell-dilaton black holes under specific conditions, extending previous results and simplifying the proof process without needing certain extensions of positive mass theorems.

Contribution

It generalizes and simplifies the uniqueness proof for static Einstein-Maxwell-dilaton black holes in specific cases, removing the need for certain assumptions used in prior work.

Findings

Uniqueness established for $ ext{α}=1$ case.

Uniqueness shown for cases with vanishing magnetic or electric fields.

Simplified proof avoids extensions of Witten's positive mass theorem.

Abstract

We prove uniqueness of static, asymptotically flat spacetimes with non-degenerate black holes for three special cases of Einstein-Maxwell-dilaton theory: For the coupling ``$\alpha = 1$'' (which is the low energy limit of string theory) on the one hand, and for vanishing magnetic or vanishing electric field (but arbitrary coupling) on the other hand. Our work generalizes in a natural, but non-trivial way the uniqueness result obtained by Masood-ul-Alam who requires both $\alpha = 1$ and absence of magnetic fields, as well as relations between the mass and the charges. Moreover, we simplify Masood-ul-Alam's proof as we do not require any non-trivial extensions of Witten's positive mass theorem. We also obtain partial results on the uniqueness problem for general harmonic maps.