CYK Tensors, Maxwell Field and Conserved Quantities for Spin-2 Field

TL;DR

This paper explores the use of Conformal Yano--Killing tensors to define and analyze conserved quantities and fluxes at null infinity in gravity, revealing obstructions to angular momentum and establishing new relations between Maxwell and spin-2 fields.

Contribution

It introduces new asymptotic charges and fluxes at null infinity using Weyl tensors, and establishes novel relations between Maxwell solutions and spin-2 fields for conserved quantities.

Findings

Defined asymptotic charges at null infinity in terms of the Weyl tensor.

Identified obstructions to the existence of angular momentum.

Constructed new conserved quantities quadratic in the Weyl tensor.

Abstract

Starting from an important application of Conformal Yano--Killing tensors for the existence of global charges in gravity, some new observations at $\scri^+$ are given. They allow to define asymptotic charges (at future null infinity) in terms of the Weyl tensor together with their fluxes through $\scri^+$. It occurs that some of them play a role of obstructions for the existence of angular momentum. Moreover, new relations between solutions of the Maxwell equations and the spin-2 field are given. They are used in the construction of new conserved quantities which are quadratic in terms of the Weyl tensor. The obtained formulae are similar to the functionals obtained from the Bel--Robinson tensor.