Classification and basic properties of circular orbits around regular black holes and solitons with the de Sitter center

Abstract

We present the detailed analysis of the circular orbits in the regular geometry with the de Sitter center which describes the regular black holes, their extreme states and the gravitational solitons (G-lumps)—non-singular non-dissipative objects without event horizons replacing naked singularities. We present general classification of the time-like and isotropic geodesics and find the existence of the special class of the isotropic geodesics which correspond to the stable circular orbits of photons whose wavelength is much less than a characteristic scale of geometry. The stable isotropic and time-like geodesics exist in the deep interiors of the gravitational solitons replacing the naked singularities. They are specified by the critical values that depend on the basic parameters including those characterizing the interior de Sitter vacuum, and can serve as the diagnostic tool for the spacetime structure of interiors of the regular black holes and solitons.