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We study the basic properties of the circular equatorial orbits for the regular axially symmetric solutions, obtained with using the Gürses–Gürsey formalism which includes the Newman–Janis algorithm, from regular spherically symmetric metrics of the Kerr–Schild class specified by Ttt=Trr. Solutions of this class describe regular rotating black holes and spinning solitons replacing naked singularities. All these objects have the interior de Sitter equatorial disk, and can have two kinds of interiors determined by the energy conditions. One of them contains an additional interior de Sitter vacuum S-surface with the de Sitter disk as a bridge, whose internal cavities are filled with a phantom fluid. We study in detail the innermost equatorial circular orbits and show that in the field of spinning solitons, the innermost orbits exist within ergoregions related to phantom regions. We show also that around spinning solitons there can exist four corotating light rings and around a regular black hole, one corotating light ring, which is stable for a certain class of black holes. For all objects there exists one counterrotating light ring.

Classification of Circular Equatorial Orbits around Regular Rotating Black Holes and Solitons with the de Sitter/ Phantom Interiors