Lagrange Formulation of the Symmetric Teleparallel Gravity

Abstract

We develop a symmetric teleparallel gravity model in a space-time with only the nonmetricity is nonzero, in terms of a Lagrangian quadratic in the non-metricity 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 ReissnerNordström-type solutions for certain values of the parameters. We also discuss the physical relevance of these solutions.

Weyl geometry and the nonlinear mechanics of distributed point defects

“…In order to find a solution, we follow the procedure in (Adak & Sert 2005;Yavari & Goriely 2012) and start by an ansatz for the material coframe field. We then find a flat connection, which is torsion-free but has a non-vanishing non-metricity compatible with the given point defect distribution.…”

The quadratic symmetric teleparallel gravity in two dimensions

“…We see that the singularity structure of the above solution of STPG is basically similar to that of GR [7], [10].…”

New Black Holes Solutions in a Modified Gravity

“…When c 1 = −2M and c 2 = −q 2 A 4 /6, the solution resembles that of RN with a complicated logarithmic term. This term appears in the solutions of (1 + 2)-Dimensional Teleparallel Gravity [31] and Symmetric Teleparallel Gravity [32]. Note also that this sort of term has been obtained, in f (R) theory, in the limit of the fourth post-Newtonian order correction [33, Equation …”

“…This solution is a generalization of the solution of RN-(A)dS. When A = 0 (γ 1 (r) = 0), the GR is recovered, with the solution of RN-(A)dS in (32). The exponent r of the constants terms c 2 and c 3 can take real values in general.…”