Angular momentum conservation for uniformly expanding flows

TL;DR

This paper introduces a new way to define and analyze angular momentum in space-time using surface integrals, applicable to uniformly expanding flows and incorporating gravitational radiation effects.

Contribution

It presents a novel definition of angular momentum as a surface integral compatible with any axis, and derives a conservation law involving gravitational radiation.

Findings

Angular momentum can be expressed as a surface integral involving an axial vector and twist 1-form.

A conservation equation for angular momentum is derived for uniformly expanding flows.

The equation includes an effective energy tensor for gravitational radiation.

Abstract

Angular momentum has recently been defined as a surface integral involving an axial vector and a twist 1-form, which measures the twisting around of space-time due to a rotating mass. The axial vector is chosen to be a transverse, divergence-free, coordinate vector, which is compatible with any initial choice of axis and integral curves. Then a conservation equation expresses rate of change of angular momentum along a uniformly expanding flow as a surface integral of angular momentum densities, with the same form as the standard equation for an axial Killing vector, apart from the inclusion of an effective energy tensor for gravitational radiation.