Publikace ÚTF

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

Krtouš, O., Frolov, V., P., Kubiznák, D.

In this paper we explicitly demonstrate separability of the Maxwell equations in a wide class of higherdimensional 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
journal:Nuclear Physics B

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