Covariant generalized conserved charges of General Relativity

TL;DR

This paper develops a coordinate- and frame-independent framework for conserved charges in General Relativity, linking them to conformal Killing-Yano forms and extending previous constructions.

Contribution

It introduces a covariant method to construct conserved charges in Einstein gravity, relating them to conformal Killing-Yano 2-forms and generalizing prior results.

Findings

Charges are associated with conformal Killing-Yano 2-forms.

Charges from closed conformal Killing-Yano 2-forms match previous dual charges.

The paper discusses the number of independent gravitational charges.

Abstract

Motivated by the current research of generalized symmetries and the construction of conserved charges in pure Einstein gravity linearized over Minkowski spacetime in Cartesian coordinates, we investigate, from a purely classical point of view, the construction of these charges in a coordinate- and frame-independent language in order to generalize them further. We show that all the charges constructed in that context are associated to the conformal Killing-Yano 2-forms of Minkowski spacetime. Furthermore, we prove that those associated to closed conformal Killing-Yano 2-forms are identical to the charges constructed by Kastor and Traschen for their dual Killing-Yano (d-2)-forms. We discuss the number of independent and non-trivial gravitational charges that can be constructed in this way.