Spinless Matter in Transposed-Equi-Affine Theory of Gravity

TL;DR

This paper explores the equations of motion for spinless matter within a novel gravity model featuring covariantly constant volume, proposing a new interpretation involving a variable Planck constant and revealing a universal torsion interaction.

Contribution

It derives the equations of motion for spinless matter in a transposed-equi-affine gravity model and introduces a new interpretation with a variable Planck constant.

Findings

Universal torsion interaction with massive fields.

Consistency conditions imply a variable Planck constant.

New perspective on gravity with covariantly constant volume.

Abstract

We derive and discus the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the recently proposed by A. Saa model of gravity with covariantly constant volume with respect to the transposed connection in Einstein-Cartan spaces. A new interpretation of this theory as a theory with variable Plank "constant" is suggested. We show that the consistency of the semiclassical limit of the wave equation and classical motion dictates a new definite universal interaction of torsion with massive fields.