Nonexistence of Degenerate Horizons in Static Vacua and Black Hole Uniqueness

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-Émery-Ricci bounds for static Einstein manifolds.

8 pages; minor improvements

References in corpus (1)

• Nonexistence of Extremal de Sitter Black Rings

Cited by in corpus (5)

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• Balancing Static Vacuum Black Holes with Signed Masses in 4 and 5 Dimensions
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• Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes