Nonexistence of Extremal de Sitter Black Rings

Abstract

We show that near-horizon geometries in the presence of a positive cosmological constant cannot exist with ring topology. In particular, de Sitter black rings with vanishing surface gravity do not exist. Our result relies on a known mathematical theorem which is a straightforward consequence of a type of energy condition for a modified Ricci tensor, similar to the curvature-dimension conditions for the $m$-Bakry-Émery-Ricci tensor.

arXiv comment4 pages

References in corpus (7)

• A rotating black ring in five dimensions
• Classification of near-horizon geometries of extremal black holes
• Black ring with two angular momenta
• Black Rings in (Anti)-deSitter space
• Do supersymmetric anti-de Sitter black rings exist?
• Blackfolds in (Anti)-de Sitter Backgrounds
• Black rings in global anti-de Sitter space

Cited by in corpus (9)

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• A Bakry-Émery Almost Splitting Result With Applications to the Topology of Black Holes
• On the nonexistence of extreme anti-de Sitter black rings
• Bounding Horizon Area by Angular Momentum, Charge, and Cosmological Constant in 5-Dimensional Minimal Supergravity
• N=4 Near-Horizon Geometries in D=11 Supergravity
• Degenerate Black Rings in $D=5$ Minimal Supergravity