Definitions of energy for the description of gravity as the splitting theory

TL;DR

This paper explores various definitions of energy within the splitting theory, a field-theoretic approach to gravity, comparing them with standard general relativity results and proposing corrections for better localization.

Contribution

It introduces and analyzes energy definitions in the splitting theory, comparing them with GR, and suggests improvements for energy localization in this framework.

Findings

Calculated total energy of an isolated massive body in splitting theory.

Compared splitting theory energy with Einstein and Møller pseudotensors.

Proposed corrections to energy definitions for better localization.

Abstract

We study the definitions of energy, naturally arising in the splitting theory, which is the field theoretic formulation of the Regge-Teitelboim gravity. The latter regards our spacetime as a surface embedded in a flat bulk. The splitting theory describes embedded spacetime in the language of the some field theory in a flat bulk. We consider the Noether energy-momentum tensor (EMT) and the metric EMT defined by the variation with respect to the metric of a flat bulk. We discuss a localizability of energy. Then using these EMTs we calculate the full energy of an isolated massive body. We compare the results with the standard general relativity results obtained from the Einstein energy-momentum pseudotensor (pEMT) and from the M{\o}ller pEMT. Finally, we propose the several ways of correction of the definitions of the energy in the splitting theory.