ИСТИНА

We study static spherically symmetric solutions of the Einstein equations in the presence of a non-minimally coupled scalar field and compare them with those in the space filled with a minimally coupled scalar field. We also study the Kantowski-Sachs cosmological solutions, which are connected with the static solutions by the duality relations. The main ingredient of these relations is an exchange of roles between the radial and the temporal coordinates, combined with the exchange between the spherical and hyperbolical two-dimensional geometries. A brief discussion of questions such as the relation between the Jordan and the Einstein frames and the description of the singularity crossing is also presented. The talk is based on the paper by A.Yu. Kamenshchik, E.O. Pozdeeva, A.A. Starobinsky, A. Tronconi, T. Vardanyan, G. Venturi and S.Yu. Vernov, Phys. Rev. D 98 (2018) 124028 [arXiv:1811.08213] and recent investigations.