Principal tensor strikes again: Separability of vector equations with torsion

Cayuso, Ramiro (Perimeter Institute, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada) (Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada) ; Gray, Finnian  (Perimeter Institute, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada) (Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada) ; Kubizňák, David  (Perimeter Institute, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada) (Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada) ; Margalit, Aoibheann (Perimeter Institute, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada) (Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada) ; Souza, Renato Gomes (Perimeter Institute, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada) (Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada) (ICTP South American Institute for Fundamental Research, IFT-UNESP, Sao Paulo, SP, 01140-070, Brazil) ; Thiele, Leander (Perimeter Institute, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada) (Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada)

05 July 2019

Abstract: Many black hole spacetimes with a 3-form field exhibit a hidden symmetry encoded in a torsion generalization of the principal Killing–Yano tensor. This tensor determines basic properties of such black holes while also underlying the separability of the Hamilton–Jacobi, Klein–Gordon, and (torsion-modified) Dirac field equations in their background. As a specific example, we consider the Chong–Cvetič–Lü–Pope black hole of D=5 minimal gauged supergravity and show that the torsion-modified vector field equations can also be separated, with the principal tensor playing a key role in the separability ansatz. For comparison, separability of the Proca field in higher-dimensional Kerr–NUT–AdS spacetimes (including new explicit formulae in odd dimensions) is also presented.


Published in: Physics letters B 795 (2019) 650-656 DOI: 10.1016/j.physletb.2019.07.007
License: CC-BY-3.0



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