ИСТИНА

The results of two papers of the authors [Phys.Rev.D 95 124039, Phys.Rev.D 97 064046] are presented. Properties of so-called constant curvature black holes (CCBHs) are studied. The CCBHs are compact geometrical objects in D dimensions which locally are equivalent to the anti-de Sitter (AdS) space although they differ from the global AdS space. The CCBHs are constructed by special identifications in the usual D-dimensional AdS space analogously to construction of Banados-Teitelboim-Zanelli black holes in 3 dimensions. We use the technique of counter terms elaborated for asymptotically locally AdS solutions that is based on a specially regularized action. We demonstrate that in dimensions D ≥ 4 CCBHs have zero mass and zero other conserved quantities; for the case of odd dimensions the vacuum energy cannot be interpreted as physically permissible. After rewriting the regularized action in the Euclidean version and analyzing the Helmholtz free energy we state that CCBHs have invalid thermodynamics properties. Thus the CCBHs are not observable and have no a physical sense.