Extremal vacuum black holes in higher dimensions

TL;DR

This paper investigates the near-horizon geometries of extremal vacuum black holes in higher dimensions, proving symmetry properties, constructing examples, and proposing a phase diagram for extremal black rings.

Contribution

It establishes symmetry constraints, constructs explicit near-horizon geometries, and conjectures a phase diagram for extremal vacuum black rings in higher dimensions.

Findings

Near-horizon geometries possess SO(2,1) symmetry under certain conditions.

Constructed examples include geometries from Myers-Perry black holes and boosted strings.

Proposed a phase diagram for extremal vacuum black rings in odd dimensions.

Abstract

We consider extremal black hole solutions to the vacuum Einstein equations in dimensions greater than five. We prove that the near-horizon geometry of any such black hole must possess an SO(2,1) symmetry in a special case where one has an enhanced rotational symmetry group. We construct examples of vacuum near-horizon geometries using the extremal Myers-Perry black holes and boosted Myers-Perry strings. The latter lead to near-horizon geometries of black ring topology, which in odd spacetime dimensions have the correct number rotational symmetries to describe an asymptotically flat black object. We argue that a subset of these correspond to the near-horizon limit of asymptotically flat extremal black rings. Using this identification we provide a conjecture for the exact ``phase diagram'' of extremal vacuum black rings with a connected horizon in odd spacetime dimensions greater than five.