The 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 spacetimes with specific horizon and hypersurface properties, refining the understanding of black hole uniqueness in general relativity.

Contribution

It extends the static electro-vacuum no-hair theorem by eliminating the restriction on the horizon degeneracy, through analysis of near-horizon geometries.

Findings

No static electro-vacuum black holes with both degenerate and non-degenerate horizons exist under the given conditions.

The study of near-horizon geometry is key to ruling out these configurations.

The results refine the classification of static electro-vacuum black hole solutions.

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. This is done by a careful study of the near-horizon geometry of degenerate horizons, which allows us to eliminate the last restriction of the static electro-vacuum no-hair theory.