Helicity and spin conservation in Maxwell theory and Linearized Gravity

TL;DR

This paper extends the understanding of conservation laws in linearized gravity by establishing the conservation of helicity, spin, and orbital angular momentum, drawing parallels with Maxwell theory and introducing an analog of the helicity array.

Contribution

It proves the conservation of spin and orbital angular momentum in linearized gravity and constructs an analog of the helicity array for this theory, linking it to known electromagnetic concepts.

Findings

Conservation of spin and orbital angular momentum in linearized gravity.

Construction of the helicity array analog for linearized gravity.

Establishment of parallels between gravity and Maxwell theory in terms of helicity and spin.

Abstract

A duality symmetric formulation of linearized gravity has been introduced by Barnett and used to show the conservation of helicity. However, the relation between helicity and spin as well as the separate conservation of the spin and orbital parts of angular momentum, which is known to hold in Maxwell theory, was not considered. These conservation laws are known to follow from the conservation of the so-called helicity array, an analog of the zilch tensor, which includes helicity, spin, and spin-flux or infra-zilch. In the present paper we prove the conservation of spin and orbital angular momentum for linearized gravity on Minkowski space, and construct the analog of the helicity array for linearized gravity.