Quantum dynamics of horizons in spherically symmetric spacetime with the de Sitter center

We present the systematic description of quantum dynamics of horizons in spherically symmetric spacetime with the de Sitter center [Formula: see text] on the background of the de Sitter vacuum [Formula: see text] with [Formula: see text]. Spacetime configurations are described by regular solutions of the Kerr-Schild class, specified by the condition [Formula: see text] on stress-energy tensors, satisfying in addition the Weak Energy Condition. To this class belongs the most of solutions presented in the literature. Regular spacetime configurations can have at most three horizons, the internal Cauchy horizon [Formula: see text], the event horizon [Formula: see text], and the cosmological horizon [Formula: see text]. Generic behavior of the basic thermodynamical parameters and dynamics of horizons in the course of evaporation are determined by the spacetime symmetry and basic laws of thermodynamics. Dynamical evolution is governed by quantum evaporation of horizons and involves three basic types of the end products of the horizons evaporation: (i) the thermodynamically stable nonsingular cosmological black hole with the double horizon [Formula: see text], (iI) the thermodynamically unstable cosmology with the double horizon [Formula: see text], and (iii) the absolutely thermodynamically stable triple horizon configuration [Formula: see text], distinguished by the holographic principle.