Compact regular objects from an electrified Tolman-like density: A new interior region for the Kerr-Newman spacetime

Abstract: Charged static and rotating objects as solutions of the Einstein-Maxwell field equations are obtained and studied in the present work. The full spacetime geometry is obtained by matching two spacetime regions, an interior region containing electrified matter and an exterior electrovacuum region. In the static case, the interior region contains a spherically symmetric distribution of matter constituted by a de Sitter-type perfect fluid with electric charge, whose energy density profile is given by a Tolman-like relation. The interior solution is smoothly matched with the exterior Reissner-Nordstr\"om electrovacuum solution, thus producing different kinds of objects, such as charged regular black holes and overcharged tension stars, that we analyze in detail. We also investigate the connection between the present static solution and the regular black holes with a de Sitter core presented in the work by Lemos and Zanchin [Phys. Rev. D 83, 124005 (2011)]. We then employ the G\"urses-G\"ursey metric and apply the Newman-Janis algorithm to construct a charged rotating interior geometry from the static interior solution. The resulting interior metric and the electromagnetic field are smoothly matched to the exterior Kerr-Newman electrovacuum solution, thus producing a regular interior for the exterior Kerr-Newman geometry. The main properties of the complete rotating solution are analyzed in detail, showing that different kinds of rotating objects, such as charged rotating black holes and other charged rotating objects, also emerge in this solution.