A new geometrical approach to metric-affine gravity

TL;DR

This paper introduces a novel geometrical framework for metric-affine gravity where the gravitational Lagrangian is scalar curvature, incorporating torsion and nonmetricity as dynamic variables, and shows it reduces to Einstein's equations in vacuum.

Contribution

It develops a new geometrical approach to metric-affine gravity with matter dependence on torsion and nonmetricity, deriving field equations and connecting to Einstein's theory.

Findings

Field equations derived for the theory

Reduction to Einstein equations in vacuum

Inclusion of torsion and nonmetricity as field variables

Abstract

Here we consider a metric-affine theory of gravity in which the gravitational Lagrangian is the scalar curvature. The matter action is allowed to depend also on the torsion and the nonmetricity, which are considered as the field variables together with the metric. We find the field equations of the theory and show that they reduce to Einstein equations in vacuum