The Symmetric Teleparallel Gravity

TL;DR

This paper explores symmetric teleparallel gravity, deriving equivalent Einstein-Hilbert formulations, finding spherically symmetric solutions, and analyzing their physical implications within a non-metricity-based framework.

Contribution

It introduces a method to obtain solutions in symmetric teleparallel gravity and derives Schwarzschild-like solutions, expanding understanding of non-metricity effects in gravity theories.

Findings

Derived an equivalent Einstein-Hilbert Lagrangian in STP

Obtained spherically symmetric static solutions

Identified Schwarzschild-type solutions in non-metricity-based gravity

Abstract

We study symmetric teleparallel (STP) gravity model, in which only spacetime non-metricity is nonzero. First we obtain STP equivalent Einstein-Hilbert Lagrangian and give an approach for a generic solution in terms of only metric tensor. Then we obtain a spherically symmetric static solution to the Einstein's equation in STP space-time and discuss the singularities. Finally, we study a model given by a Lagrangian 4-form quadratic in non-metricity. Thus, we seek Schwarzschild-type solutions because of its observational success and obtain some sets of solutions. Finally, we discuss physical relevance of the solutions.