Total intrinsic spin for plane gravity waves

TL;DR

This paper constructs a conserved measure of total intrinsic spin for plane gravity waves in both Ashtekar and geometrodynamics formalisms, revealing new insights into gravitational field observables.

Contribution

It introduces a novel conserved total spin quantity for plane gravity waves, linking it to known observables and physical operators within gravitational theories.

Findings

Total intrinsic spin is conserved in plane gravity waves.

The total spin is not a surface term, contrary to expectations.

The conserved spin coincides with a known observable by Husain and Smolin.

Abstract

A quantity which measures total intrinsic spin along the z axis is constructed for planar gravity (fields dependent on z and t only), in both the Ashtekar complex connection formalism and in geometrodynamics. The total spin is conserved but (surprisingly) is not a surface term. This constant of the motion coincides with one of four observables previously discovered by Husain and Smolin. Two more of those observables can be interpreted physically as raising and lowering operators for total spin.