Single-rotating Five-dimensional Near-horizon Extremal Geometry in General Relativity

TL;DR

This paper introduces a new five-dimensional near-horizon extremal geometry with a single rotation that can have finite entropy, despite existing uniqueness theorems, due to a curvature singularity breaking smoothness conditions.

Contribution

It presents a novel five-dimensional near-horizon extremal geometry with one angular momentum and finite entropy, challenging previous uniqueness theorems due to a singularity.

Findings

New five-dimensional near-horizon extremal geometry with finite entropy.

Presence of a curvature singularity at one pole.

Breaks smoothness conditions of existing uniqueness theorems.

Abstract

The geometries with SL$(2,\mathbb{R})$ and some axial U$(1)$ isometries are called ``near-horizon extremal geometries" and are found usually, but not necessarily, in the near-horizon limit of the extremal black holes. We present a new member of this family of solutions in five-dimensional Einstein-Hilbert gravity that has only one nonzero angular momentum. In contrast with the single-rotating Myers-Perry extremal black hole and its near-horizon geometry in five dimensions, this solution may have a nonvanishing and finite entropy. Although there is a uniqueness theorem that prohibits the existence of such single-rotating near-horizon geometries in five-dimensional general relativity, this solution has a curvature singularity at one of the poles, which breaks the smoothness conditions in the theorem.