Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity

TL;DR

This paper introduces a quasigroup framework for defining conserved quantities like energy and momentum in general relativity, resolving supertranslation ambiguities and applying it to asymptotically flat spacetimes.

Contribution

It develops a novel quasigroup approach to conservation laws in general relativity, reducing asymptotic symmetries to a Poincaré quasigroup and defining associated Noether charges.

Findings

Conserved quantities are linear on Poincaré quasigroup generators.

The approach eliminates supertranslation ambiguities.

Conserved quantities vanish in Minkowski spacetime.

Abstract

A new quasigroup approach to conservation laws in general relativity is applied to study asymptotically flat at future null infinity spacetime. The infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to the Poincar\'e quasigroup and the Noether charge associated with any element of the Poincar\'e quasialgebra is defined. The integral conserved quantities of energy-momentum and angular momentum are linear on generators of Poincar\'e quasigroup, free of the supertranslation ambiguity, posess the flux and identically equal to zero in Minkowski spacetime.