Basic Generic Properties of Regular Rotating Black Holes and Solitons

We present a systematic description of the basic generic properties of regular rotating black holes and solitons (compact nonsingular nondissipative objects without horizons related by self-interaction and replacing naked singularities). Rotating objects are described by axially symmetric solutions typically obtained by the Gurses-Guursey algorithm, which is based on the Trautman-Newman techniques and includes the Newman-Janis complex transformation, from spherically symmetric solutions of the Kerr-Schild class specified by T-t(t) = T-r(r) (p(r) = -rho). Regular spherical solutions of this class satisfying the weak energy condition have obligatory de Sitter center. Rotation transforms de Sitter center into the equatorial de Sitter vacuum disk. Regular solutions have the Kerr or Kerr-Newman asymptotics for a distant observer, at most two horizons and two ergospheres, and two different kinds of interiors. For regular rotating solutions originated from spherical solutions satisfying the dominant energy condition, there can exist the interior S-surface of de Sitter vacuum which contains the de Sitter disk as a bridge. In the case when a related spherical solution violates the dominant energy condition, vacuum interior of a rotating object reduces to the de Sitter disk only.