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

¹ Department of Physics, Nagoya University - Nagoya 464-8602, Japan
² Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University Nagoya 464-8602, Japan
³ ICREA - Passeig Luis Companys, 23, 08010 Barcelona, Spain
⁴ Institute of Space Sciences (IEEC-CSIC) - C. Can Magrans s/n, 08193 Barcelona, Spain
⁵ Lab. Theor. Cosm., TUSUR - 634050 Tomsk, Russia

Received: 4 April 2020
Accepted: 20 April 2020

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.