Lagrange formulation of the symmetric teleparallel gravity

TL;DR

This paper formulates a symmetric teleparallel gravity model using a quadratic non-metricity Lagrangian, deriving solutions like Schwarzschild and Reissner-Nordström types, relevant for understanding alternative gravity theories.

Contribution

It introduces a Lagrangian-based symmetric teleparallel gravity framework focusing on non-metricity, and derives exact solutions with potential observational implications.

Findings

Derived Schwarzschild-type solutions in the model

Obtained Schwarzschild-de Sitter and Reissner-Nordström solutions

Discussed physical relevance of the solutions

Abstract

We develop a symmetric teleparallel gravity model in a space-time with only the non-metricity 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 Reissner-Nordstr\"{o}m-type solutions for certain values of the parameters. We also discuss the physical relevance of these solutions.