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

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.