WANDs of the Black Ring

TL;DR

This paper investigates the algebraic classification of the Weyl tensor in black ring solutions, identifying their algebraic types and null directions, and comparing them with the Myers-Perry solution.

Contribution

It determines necessary algebraic conditions for black ring solutions and classifies their Weyl tensor types, revealing their algebraic specialness and relation to known solutions.

Findings

Black ring solution is algebraically special, of type I_i.

On the horizon, the black ring is of type II.

Myers-Perry solution is of type D.

Abstract

Necessary conditions for various algebraic types of the Weyl tensor are determined. These conditions are then used to find Weyl aligned null directions for the black ring solution. It is shown that the black ring solution is algebraically special, of type I_i, while locally on the horizon the type is II. One exceptional subclass - the Myers-Perry solution - is of type D.