Nonexistence of Extremal de Sitter Black Rings

TL;DR

This paper proves that extremal de Sitter black rings with ring topology cannot exist due to geometric and energy condition constraints, specifically ruling out de Sitter black rings with zero surface gravity.

Contribution

It establishes a nonexistence theorem for extremal de Sitter black rings using a mathematical approach based on energy conditions and modified Ricci tensor properties.

Findings

Extremal de Sitter black rings with ring topology do not exist.

The proof relies on a theorem related to the curvature-dimension condition for a modified Ricci tensor.

De Sitter black rings with vanishing surface gravity are ruled out.

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-\'Emery-Ricci tensor.