Tensor-Scalar Torsion

TL;DR

This paper develops a gravity theory incorporating torsion, constructed from a potential and a scalar field, deriving field equations and demonstrating conservation of angular momentum and spin.

Contribution

It introduces a novel torsion-based gravity model with a scalar field and derives consistent field equations and conservation laws.

Findings

Derived field equations for the torsion-based gravity model

Established conservation law for angular momentum and spin

Integrated material action into the torsion framework

Abstract

A theory of gravity with torsion is examined in which the torsion tensor is constructed from the exterior derivative of an antisymmetric rank two potential plus the dual of the gradient of a scalar field. Field equations for the theory are derived by demanding that the action be stationary under variations with respect to the metric, the antisymmetric potential, and the scalar field. A material action is introduced and the equations of motion are derived. The correct conservation law for rotational angular momentum plus spin is observed to hold in this theory.