Geodesics and Symmetries of Doubly-Spinning Black Rings

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.

Minor corrections/clarifications and references added, results of paper unchanged. Accepted for publication by Class. Quant. Grav. (26 pages, 5 figures)

References in corpus (10)

• Near-horizon symmetries of extremal black holes
• General Kerr-NUT-AdS Metrics in All Dimensions
• Hidden symmetries, null geodesics, and photon capture in the Sen black hole
• Bicycling Black Rings
• Black ring with two angular momenta
• Boundary Value Problem for Black Rings
• Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime
• Particle Motion in the Rotating Black Ring Metric
• Five-Dimensional Black Hole Capture Cross-Sections
• On Universality of Ergoregion Mergers

Cited by in corpus (8)

• Dynamics of test particles in the general five-dimensional Myers-Perry spacetime
• Geodesic Motion in the Singly Spinning Black Ring Spacetime
• Geodesic Motion in the (Charged) Doubly Spinning Black Ring Spacetime
• Stable Bound Orbits around Black Rings
• Chaos in Geodesic Motion around a Black Ring
• A Charged Doubly Spinning Black Ring
• Algebraic classification of five-dimensional spacetimes using scalar invariants
• Integrability of Particle System around a Ring Source as the Newtonian Limit of a Black Ring