Geodesics and Symmetries of Doubly-Spinning Black Rings

TL;DR

This paper explores the geometric and symmetry properties of doubly-spinning black ring spacetimes, focusing on geodesic separability, coordinate construction, and related tensor structures, revealing differences between singly and doubly-spinning cases.

Contribution

It demonstrates the separability of Hamilton-Jacobi equations for null geodesics in doubly-spinning black rings and links this to conformal Killing tensors, highlighting new geometric insights.

Findings

Separability of Hamilton-Jacobi equation for null geodesics in ergoregion

Construction of horizon-covering coordinates based on geodesics

Existence of conformal Killing tensor in reduced spacetime, but not conformal Killing-Yano tensor in doubly-spinning case

Abstract

This paper studies various properties of the Pomeransky-Sen'kov doubly-spinning black ring spacetime. I discuss the structure of the ergoregion, and then go on to demonstrate the separability of the Hamilton-Jacobi equation for null, zero energy geodesics, which exist in the ergoregion. These geodesics are used to construct geometrically motivated coordinates that cover the black hole horizon. Finally, I relate this weak form of separability to the existence of a conformal Killing tensor in a particular 4-dimensional spacetime obtained by Kaluza-Klein reduction, and show that a related conformal Killing-Yano tensor only exists in the singly-spinning case.