Energy momentum tensor of a non-minimally coupled scalar from the equivalence of the Einstein and Jordan frames

TL;DR

This paper presents a method to uniquely compute the energy-momentum tensor in non-minimally coupled scalar-tensor theories by leveraging the equivalence between Einstein and Jordan frames.

Contribution

It introduces an algorithm that resolves the arbitrariness in EMT calculation for NMCT using frame equivalence.

Findings

Provides a systematic procedure for EMT construction in NMCT

Ensures unique EMT determination in non-minimally coupled theories

Bridges Einstein and Jordan frame formulations effectively

Abstract

Unlike the minimally coupled gravity theory where matter is coupled with gravity in such a manner so that one can differentiate the matter and gravity sector uniquely, the non-minimally coupled theories (NMCT) are distinguished by the intermingling of two. As a consequence of this the calculation of the energy momentum tensor (EMT) in NMCT is beset with an arbitrariness. In this paper we provide an algorithm based on the well known equivalence between Jordan frame and Einstein frame formulations which enables us to construct the EMT for NMCT in a unique way.