On the nonexistence of extreme anti-de Sitter black rings

TL;DR

This paper proves that five-dimensional extreme anti-de Sitter black rings with biaxial symmetry cannot exist, by showing the nonexistence of certain near-horizon geometries with ring topology and a nonzero cosmological constant.

Contribution

It establishes a nonexistence result for a class of five-dimensional extreme anti-de Sitter black rings with biaxial symmetry.

Findings

No five-dimensional extreme anti-de Sitter black rings with biaxial symmetry exist.

Nonexistence of near-horizon geometries with ring topology and nonzero cosmological constant.

Supports uniqueness of black hole solutions in this setting.

Abstract

We prove that five-dimensional extreme anti-de Sitter black ring solutions to the vacuum Einstein equations that admit biaxial symmetry do not exist. This is established by demonstrating the nonexistence of five-dimensional, biaxisymmetric, vacuum near-horizon geometries of extreme horizons with a nonzero cosmological constant and ring topology.