Nonexistence of Degenerate Horizons in Static Vacua and Black Hole Uniqueness

TL;DR

This paper proves that in higher-dimensional static vacuum spacetimes with positive cosmological constant, degenerate horizons cannot exist, and similarly, asymptotically flat solutions lack degenerate horizons, using multiple geometric methods.

Contribution

It establishes the nonexistence of degenerate horizons in static vacuum spacetimes with positive cosmological constant and in asymptotically flat cases, providing several independent proofs.

Findings

Degenerate horizons do not exist in static vacuum spacetimes with positive cosmological constant.

Asymptotically flat static vacuum solutions cannot have degenerate horizons.

Multiple geometric proofs confirm the nonexistence results.

Abstract

We show that in any spacetime dimension $D\ge 4$, degenerate components of the event horizon do not exist in static vacuum configurations with positive cosmological constant. We also show that without a cosmological constant asymptotically flat solutions cannot possess a degenerate horizon component. Several independent proofs are presented. One proof follows easily from differential geometry in the near-horizon limit, while others use Bakry-\'Emery-Ricci bounds for static Einstein manifolds.