Killing-Yano Cotton currents

Abstract

We discuss conserved currents constructed from the Cotton tensor and (conformal) Killing-Yano tensors (KYTs). We consider the corresponding charges generally and then exemplify with the four-dimensional Plebański-Demiański metric where they are proportional to the sum of the squares of the electric and the magnetic charges. As part of the derivation, we also find the two conformal Killing-Yano tensors of the Plebański-Demiański metric in the recently introduced coordinates of Podolsky and Vratny. The construction of asymptotic charges for the Cotton current is elucidated and compared to the three-dimensional construction in Topologically Massive Gravity. For the three-dimensional case, we also give a conformal superspace multiplet that contains the Cotton current in the bosonic sector. In a mathematical section, we derive potentials for the currents, find identities for conformal KYTs and for KYTs in torsionful backgrounds.

Uses of Killing and Killing-Yano Tensors

“…The identity (29) may be generalized to CKYTs (19) (as well as to geometries with torsion, see [21]). For a second rank CKYT , it reads…”

“…Above we have focused on the KT current. Another current, the Killing-Yano Cotton current, was recently constructed in [21]. Here we briefly describe this current.…”

“…Ulf Lindström with normal to the spacelike surface Σ. We apply this construction to the Plebański-Demiański metric where we can carry out the integration for certain values of the metric parameters in [21].…”

“…Of particular interest in the present context is the relation of Killing-Yano tensors to asymptotic conserved charges [18,19]. In this presentation we will give lightning reviews of a few of these topics and report on some new results [20,21] and [22].…”

“…In [30], it is used to define asymptotic charges using a current based on the energymomentum tensor and an asymptotic Killing vector. In [21], we compare it to our Cotton current in 3 with some interesting results.…”