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arXiv · 1906.10072

Principal Tensor Strikes Again: Separability of Vector Equations with Torsion

Ramiro Cayuso·Finnian Gray·David Kubiznak·Aoibheann Margalit·Renato Gomes Souza·Leander Thiele
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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--Cveti\v{c}--L\"u--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.

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Ramiro Cayuso, Finnian Gray, David Kubiznak, Aoibheann Margalit, Renato Gomes Souza, Leander Thiele. 2019-06-24. Principal Tensor Strikes Again: Separability of Vector Equations with Torsion. https://doi.org/10.1016/j.physletb.2019.07.007

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