Separation of variables in Maxwell equations in Plebanski-Demianski spacetime

TL;DR

This paper generalizes a recent method for separating Maxwell's equations in Kerr-(A)dS spacetimes to any off-shell metric with a principal Killing-Yano tensor, demonstrating separability in Plebanski-Demianski spacetime.

Contribution

It introduces a covariant formulation of Lunin's ansatz for vector potential, extending the separation of variables technique to broader classes of spacetimes.

Findings

Separable Maxwell's equations in Plebanski-Demianski spacetime.

Covariant formulation of Lunin's ansatz.

Applicability to off-shell metrics with principal Killing-Yano tensor.

Abstract

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.