Lagrange formulation of the symmetric teleparallel gravity

Abstract

We develop a symmetric teleparallel gravity model in a space-time with only the nonmetricity as nonzero, in terms of a Lagrangian quadratic in the nonmetricity tensor. We present a detailed discussion of the variations that may be used for any gravitational formulation. We seek Schwarzschild-type solutions because of its observational significance and obtain a class of solutions that includes Schwarzschild-type, Schwarzschild-de Sitter-type, and Reissner-Nordström-type solutions for certain values of the parameters. We also discuss the physical relevance of these solutions. © World Scientific Publishing Company.