Evolution of angular momentum and center of mass at null infinity

TL;DR

This paper derives evolution formulas for angular momentum and center of mass at null infinity, revealing invariance properties and conservation laws that extend classical gravitational radiation results.

Contribution

It introduces new evolution equations for conserved quantities at null infinity expressed via shear and news potentials, highlighting supertranslation invariance and duality.

Findings

Supertranslation invariance of fluxes of CWY conserved quantities

A Christodoulou-like conservation law for angular momentum

A duality paradigm for null infinity

Abstract

We study how conserved quantities such as angular momentum and center of mass evolve with respect to the retarded time at null infinity, which is described in terms of a Bondi-Sachs coordinate system. These evolution formulae complement the classical Bondi mass loss formula for gravitational radiation. They are further expressed in terms of the potentials of the shear and news tensors. The consequences that follow from these formulae are (1) Supertranslation invariance of the fluxes of the CWY conserved quantities. (2) A conservation law of angular momentum \`a la Christodoulou. (3) A duality paradigm for null infinity. In particular, the supertranslation invariance distinguishes the CWY angular momentum and center of mass from the classical definitions.