Separation of Maxwell equations in Kerr-NUT-(A)dS spacetimes
| Autor: | Krtouš, Pavel, Frolov, Valeri P., Kubizňák, David |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Nucl. Phys. B 934, 7-38 (2018) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2018.06.019 |
| Popis: | 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 separability 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. Comment: 36 pages, no figures [v2: a note on the Proca field added; v3: misprint corrections, references updated] |
| Databáze: | arXiv |
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