Principal Tensor Strikes Again: Separability of Vector Equations with Torsion

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.

arXiv comment8 pages

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Cited by in corpus (7)

• Massive vector fields in Kerr--Newman and Kerr--Sen black hole spacetimes
• Electromagnetic fields on Kerr spacetime, Hertz potentials and Lorenz gauge
• Excitations of the Myers-Perry Black Holes
• On symmetry operators for the Maxwell equation on the Kerr-NUT-(A)dS spacetime
• Hidden symmetry and the separability of the Maxwell equation on the Wahlquist spacetime
• Separation of variables in the WZW models
• Vector perturbations of Kerr-AdS${}_5$ and the Painlevé VI transcendent