Separation of variables in Maxwell equations in Plebański-Demiański spacetime

A new method for separating variables in the Maxwell 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 Plebański–Demiański family of spacetimes. The new method of separation of variables is quite different from the standard approach based on the Newman–Penrose formalism.