Abstract
We study properties of a recently proposed new ansatz for separation of variables in the Maxwell equations in four dimensional Kerr-NUT-(A)dS spacetime. We demonstrate that a dual field, which is also a solution of the source-free Maxwell equations, can be presented in a similar form. This result implies that the corresponding separated equations possess a discrete symmetry under a special transform of the separation parameters.
Highlights
Solving wave equations in a curved spacetime is an important problem
The separation of variables in the Maxwell equations in the four-dimensional Kerr spacetime plays an important role in the study of the propagation of electromagneric waves in the vicinity of rotating black holes
Method developed by Teukolski in 1972 [1,2] has been widely used for this purpose. This method is closely related to the algebraical structure of the background metric, and it can be applied to the vacuum-type D solutions of the Einstein equations
Summary
Solving wave equations in a curved spacetime is an important problem. Practically all information available to observers concerning the properties of massive compact objects is obtained by studying electromagnetic radiation from these objects or matter surrounding them. Separability of the Maxwell equations in the Kerr spacetime, demonstrated by Teukolsky [1,2], allows one to reduce a rather complicated problem of studying electromagnetic field propagation in the black hole spacetime to studying solutions of a set of the second order ordinary differential equations (ODE). Lunin demonstrated that the integrability conditions of the Maxwell equations in the Myers-Perry metrics, which are third order relations for Z, reduce to decoupled second order ODE for functions of the independent variables, which enter as a product in Z Later, this construction was generalized to any off-shell Kerr-NUT-(A)dS spacetime [9,10]. As a consequence of these results, we shall demonstrate that the μ-separated equations admit a discrete symmetry transformation which preserve their form
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