Conformal Yano-Killing tensor for the Kerr metric and conserved quantities

TL;DR

This paper explores conformal Yano-Killing tensors in Kerr spacetime, deriving explicit forms and a new conserved quantity related to the Weyl tensor, offering insights into conserved quantities in general relativity.

Contribution

It introduces explicit conformal Killing tensors in Kerr spacetime and constructs a novel conserved quantity quadratic in the Weyl tensor, linking spin-2 fields and Maxwell solutions.

Findings

Explicit conformal Killing tensors in Kerr spacetime.

A new conserved quantity quadratic in the Weyl tensor.

Comparison with the Bel-Robinson tensor.

Abstract

Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed. Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime are obtained from the Yano--Killing tensor. The relation between spin-2 fields and solutions to the Maxwell equations is used in the construction of a new conserved quantity which is quadratic in terms of the Weyl tensor. The formula obtained is similar to the functional obtained from the Bel--Robinson tensor and is examined in Kerr spacetime. A new interpretation of the conserved quantity obtained is proposed.