Torsion and Nonmetricity in Scalar-Tensor Theories of Gravity

TL;DR

This paper demonstrates that in scalar-tensor theories of gravity, the gravitational field equations are equivalent whether nonmetricity or torsion is non-zero, given an action with scalar curvature and scalar fields.

Contribution

It establishes the equivalence of field equations in scalar-tensor gravity theories regardless of whether nonmetricity or torsion is present.

Findings

Field equations are identical with non-zero torsion or nonmetricity.

The equivalence holds for actions with scalar curvature and scalar fields.

The result simplifies understanding of geometric structures in gravity theories.

Abstract

We show that the gravitational field equations derived from an action composed of i) an arbitrary function of the scalar curvature and other scalar fields plus ii) connection-independent kinetic and source terms, are identical whether one chooses nonmetricity to vanish and have non-zero torsion or vice versa.