Novel cosmological and black hole solutions in Einstein and higher-derivative gravity in two dimensions

Abstract

We consider cosmological and black hole solutions in the Einstein and higher-derivative gravity in two dimensions where the theory is formulated first in D dimensions. In the limit that D tends to 2 with simultaneous singular rescaling of the scalar curvature coupling constant as , we get the novel Einstein and higher-derivative gravity. Due to non-trivial contribution of scalar curvature which is topological invariant in exactly two dimensions to gravitational equations in the two-dimensional limit one gets novel cosmological and black hole solutions. In particular, the de Sitter and radiation-dominated universe and the Schwarzschild–de Sitter and Schwarzschild–anti-de Sitter black hole solutions are obtained and their properties are discussed.