Intrinsic vanishing of energy and momenta in a universe

TL;DR

This paper introduces a new method to define conserved energy and momenta in general relativity for universes that are not asymptotically flat, focusing on creating a consistent framework for universes with vanishing total 4-momenta.

Contribution

It proves the existence of special coordinates where conserved momenta vanish, enabling a consistent treatment of creatable universes with zero total 4-momenta.

Findings

Existence of special Gauss coordinates with vanishing conserved momenta.

Formalism recovers known results for FLRW universes.

Framework facilitates analysis of universes with zero total energy and momentum.

Abstract

We present a new approach to the question of properly defining energy and momenta for non asymptotically Minkowskian spaces in general relativity, in the case where these energy and momenta are conserved. In order to do this, we first prove that there always exist some special Gauss coordinates for which the conserved linear and angular three-momenta vanish. This allows us to consider the case of creatable universes (the universes whose proper 4-momenta vanish) in a consistent way, which is the main interest of the paper. When applied to the Friedmann-Lema{\^{\i}}tre-Robertson-Walker case, perturbed or not, our formalism leads to previous results, according to most literature on the subject. Some future work that should be done is mentioned.