A Quasigroup Approach for Conservation Laws in Asymptotically Flat Spacetimes

TL;DR

This paper applies a quasigroup approach to conservation laws in general relativity, reducing asymptotic symmetries to a Poincare quasigroup and defining conserved quantities like energy and angular momentum.

Contribution

It introduces a novel quasigroup framework for conservation laws, providing new definitions of angular momentum and mass reference frames in asymptotically flat spacetimes.

Findings

Reduction of Newman-Unti group to Poincare quasigroup

Definition of supertranslation-ambiguity-free angular momentum

Expression of momentum and angular momentum via Komar formula

Abstract

In the framework of the quasigroup approach to conservation laws in general relativity, we show how the infinite-parametric Newman-Unti group of asymptotic symmetries can be reduced to the Poincare quasigroup. We compute Noether's charges associated with any element of the Poincare quasialgebra. The integral conserved quantities of energy momentum and angular momentum, being linear on generators of the Poincare quasigroup, are identically equal to zero in Minkowski spacetime. We present a definition of the angular momentum free of the supertranslation ambiguity. We provide an appropriate notion of intrinsic angular momentum and a description of the mass reference frame's center at future null infinity. Finally, in the center of mass reference frame, the momentum and angular momentum are defined by the Komar expression.