A field theoretic approach to the energy momentum tensor for theories coupled with gravity

TL;DR

This paper introduces a field-theoretic algorithm to derive the energy-momentum tensor for theories coupled with gravity, clarifying its relation to energy-momentum balance and aiding in non-minimal coupling analysis.

Contribution

It presents a novel algorithm based on an auxiliary field theory to obtain the energy-momentum tensor in gravitationally coupled theories, applicable to both minimal and non-minimal couplings.

Findings

Provides a systematic method for deriving EMT in gravity theories.

Clarifies the connection between EMT variation and energy-momentum conservation.

Enhances understanding of non-minimally coupled gravity theories.

Abstract

We provide a field-theoretic algorithm of obtaining energy momentum tensor (EMT) for gravitationally coupled theories. The method is based on an auxiliary field theory and equally applicable to both minimal and non-minimal coupling. The algorithm illuminates the connection between the EMT, obtained by functional variation of the metric, and local balance of energy and momentum. Our method is of cardinal value for the proper identification of the EMT in context of non-minimally coupled gravity theories.