Orbits of Particles and Photons around Regular Rotating Black Holes and Solitons

We briefly overview the basic properties and generic behavior of circular equatorial particle orbits and light rings around regular rotating compact objects with dark energy interiors, which are described by regular metrics of the Kerr–Schild class and include rotating black holes and self-gravitating spinning solitons replacing naked singularities. These objects have an internal de Sitter vacuum disk and can have two types of dark interiors, depending on the energy conditions. The first type reduces to the de Sitter disk, the second contains a closed de Sitter surface and an S surface with the de Sitter disk as the bridge and an anisotropic phantom fluid in the regions between the S surface and the disk. In regular geometry, the potentials decrease from V(r)→∞ to their minima, which ensures the existence of the innermost stable photon and particle orbits that are essential for processes of energy extraction occurring within the ergoregions, which for the second type of interiors contain the phantom energy. The innermost orbits provide a diagnostic tool for investigation of dark interiors of de Sitter–Kerr objects. They include light rings which confine these objects and ensure the most informative observational signature for rotating black holes presented by their shadows