Separation of Maxwell equations in Kerr–NUT–(A)dS spacetimes

Abstract

In this paper we explicitly demonstrate separability of the Maxwell equations in a wide class of higher-dimensional metrics which include the Kerr–NUT–(A)dS solution as a special case. Namely, we prove such separability for the most general metric admitting the principal tensor (a non-degenerate closed conformal Killing–Yano 2-form). To this purpose we use a special ansatz for the electromagnetic potential, which we represent as a product of a (rank 2) polarization tensor with the gradient of a potential function, generalizing the ansatz recently proposed by Lunin. We show that for a special choice of the polarization tensor written in terms of the principal tensor, both the Lorenz gauge condition and the Maxwell equations reduce to a composition of mutually commuting operators acting on the potential function. A solution to both these equations can be written in terms of an eigenfunction of these commuting operators. When incorporating a multiplicative separation ansatz, it turns out that the eigenvalue equations reduce to a set of separated ordinary differential equations with the eigenvalues playing a role of separability constants. The remaining ambiguity in the separated equations is related to an identification of D−2 polarizations of the electromagnetic field. We thus obtained a sufficiently rich set of solutions for the Maxwell equations in these spacetimes.