Kerr-Newman outside a rotating de Sitter-type core: Different types of interior electromagnetic fields and currents

Abstract

We investigate the structure of interior electromagnetic fields compatible with the exterior Kerr-Newman geometry when regular interior geometries for describing regular black hole solutions are considered. Working within the Gürses-Gürsey framework and considering a rotating de Sitter-type geometry in the interior region, we analyze a particular class of electromagnetic fields aligned with the principal null directions and satisfying Maxwell electrodynamics. We show that, within such a class of interior electromagnetic fields, no well-behaved interior electromagnetic field can be supported in the absence of electromagnetic currents. Moreover, we show that for the same interior and exterior geometries, different types of interior electromagnetic fields and charge distributions, together with different charge densities on the rotating boundary shell, can be constructed while matching the same exterior Kerr-Newman electromagnetic field. This results highlight the non-uniqueness of the interior electromagnetic structure compatible with a given Kerr-Newman exterior. For a particular choice of interior electromagnetic fields we show that the de Sitter fluid can be interpreted as being electrically polarized by the rotating charged shell. In this case, the interior region contains no net electric charge, which is instead concentrated entirely on the shell, and the interior medium behaves as a perfect conductor with infinite conductivity. In a second choice for the electromagnetic field, we show that the polarized de Sitter fluid also contributes to the total electric charge, with the interior medium acting as a nonisotropic conductor.

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