Nonexistence of Degenerate Horizons in Static Vacua and Black Hole Uniqueness
arXiv:1710.09669 · doi:10.1016/j.physletb.2017.12.044
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-Ãmery-Ricci bounds for static Einstein manifolds.
8 pages; minor improvements