CYK tensors, Maxwell field and conserved quantities for the spin-2 field

Abstract

Starting from an important application of Conformal Yano-Killing tensors for the existence of global charges in gravity (which has been performed in [17] and [18]), some new observations at I + are given. They allow to define asymptotic charges (at future null infinity) in terms of the Weyl tensor together with their fluxes through I + . 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.

Killing-Yano Tensors and Angular Momentum

“…By direct calculations we observed that (18) and (19) admit three Killing vectors given by (13) and a (KY) tensor having the following non-zero components…”

“…In the last yers a huge effort was devoted for analyzing the importance of (KY) tensors [9,10,11,12,13,14,15] in several areas but there are relatively few manifolds of physical interest admitting these tensors. This drawback is mainly because (KY) tensors are antisymmetric and their equations impose restrictions on the manifold structure [8].…”

Conformal Yano–Killing tensors for the Taub–NUT metric

“…Conserved quantities which are linear with respect to CYK tensor were investigated many times (cf. [6], [7], [9], [10], [12], [15], [16]). On the other hand, quadratic charges are less known and have usually been examined in terms of the Bel-Robinson tensor (see e.g.…”

Mixed Ge-Si Dimer Formation in Ge/Si(100) and Si/Ge(100) Growth

“…According to [28] one can define, in terms of spacetime curvature, two kinds of conserved quantities with the help of conformal Yano-Killing tensors (or shortly CYK tensors, sometimes called conformal Killing forms or twistor forms, see e.g. [30,38,39]).…”

“…The first kind is linear and the second quadratic with respect to the Weyl tensor, but a basis for both of them is the Maxwell field. Conserved quantities which are linear with respect to the CYK tensor were investigated many times (cf [1,21,22,25,26,28,35,36]). On the other hand, quadratic charges are less known and have usually been examined in terms of the Bel-Robinson tensor (see e.g.…”