Kerr-Newman outside a rotating de Sitter-type core: A rotating version of the Lemos-Zanchin electrically charged solution

Abstract: A rotating version of the solution of the Einstein-Maxwell system of equations modeling static electrically charged regular black holes by Lemos and Zanchin [Phys. Rev. D 83, 124005 (2011)] is obtained in the present work. The full rotating geometry consists of the Kerr-Newman exterior geometry outside a rotating de Sitter-type core, with an electrically charged spheroidal shell at the boundary. The properties of the entire rotating solution, such as electromagnetic charge and current distributions, curvature regularity, energy-momentum tensor, and energy conditions, are thoroughly examined, revealing various types of charged rotating objects. We also study in detail the possible electromagnetic fields allowed in the interior region of the spheroidal shell of charge. By assuming that the interior geometry is described by the G\"urses-G\"ursey metric with an arbitrary mass function, we show that no well-behaved electromagnetic field is allowed in the interior region if it is devoid of electromagnetic sources. We also note that, although the overall electric charge of the static solution is preserved, the arbitrariness of the algorithm allows us to propose different electromagnetic fields and charge distributions for the same geometry of the interior region, together with different charge densities on the rotating boundary shell, without changing the exterior Kerr-Newman solution. For a particular choice of the interior electromagnetic fields, we show that it is possible to interpret the rotating de Sitter fluid as being electrically polarized due to the presence of the rotating charged spheroidal shell, despite the absence of net electric charge within the interior region, which is instead concentrated solely on the charged shell, with the interior medium behaving as a perfect conductor with infinite conductivity.