Towards a classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior

TL;DR

This paper proves the non-existence of certain static electro-vacuum black hole space-times with specific horizon properties under a charge sign condition, extending previous uniqueness theorems.

Contribution

It extends the classification of static electro-vacuum space-times by including cases with both degenerate and non-degenerate horizons under a charge sign assumption.

Findings

Non-existence of such space-times under given conditions

Extension of previous uniqueness theorems to mixed horizon types

Conditions on charges of degenerate horizon components

Abstract

We show that static electro-vacuum black hole space-times containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non-degenerate components of the event horizon do not exist, under the supplementary hypothesis that all degenerate components of the event horizon have charges of the same sign. This extends previous uniqueness theorems of Simon and Masood-ul-Alam (where only non-degenerate horizons were allowed) and Heusler (where only degenerate horizons were allowed).