# Gravity with torsion in non-conservative Maxwell-like gauge approach

## TL;DR

This paper generalizes gauge theories inspired by Maxwell theory to include torsion in gravity, leading to modified equations with non-conserved energy-momentum, allowing new matter-energy couplings.

## Contribution

It introduces a novel gauge-theoretic approach to gravity that incorporates torsion and non-conservation of energy-momentum from fundamental principles.

## Key findings

- Derived modified gravitational equations with torsion.
- Demonstrated non-conservation of energy-momentum tensor.
- Proposed new matter-energy coupling mechanisms.

## Abstract

In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such class of theories is based on few principles related to different orders of commutators between covariant derivatives. Their physical meaning is very simple, and lies in stating that the local transformations of a suitable substratum (the space-time or a particular phase space) and the imposed constraints define a "compensative mechanism" or the "interaction" we want to characterize. After a mathematical introduction, we apply this approach to a modified theory of gravity, in which the algebra of operators of covariant derivatives leads to an additional term in the equation of motion associated with the non-conservation of the energy-moment tensor. This offers the possibility to include, without ad hoc physical assumptions and directly from the formalism, new forms of coupling between matter and energy and the expression of the mixing between gravity and torsion.