A new method for separating variables in Maxwell's equations in four- and higher-dimensional Kerr-(A)dS spacetimes proposed recently by Lunin is generalized to any off-shell metric that admits a principal Killing-Yano tensor. The key observation is that Lunin's ansatz for the vector potential can be formulated in a covariant form - in terms of the principal tensor. In particular, focusing on the four-dimensional case we demonstrate separability of Maxwell's equations in the Kerr-NUT-(A)dS and the Plebanski-Demianski family of spacetimes. The new method of separation of variables is quite different from the standard approach based on the Newman-Penrose formalism.
Frolov, V. P., Krtouš, P., & Kubizňák, D. (2018). Separation of variables in Maxwell equations in Plebański-Demiański spacetime. Physical Review D, 97(10). https://doi.org/10.1103/PhysRevD.97.101701