New currents with Killing-Yano tensors

Abstract

New relations involving the Riemann, Ricci and Einstein tensors that have to hold for a given geometry to admit Killing-Yano tensors are described. These relations are then used to introduce novel conserved "currents" involving such Killing-Yano tensors. For a particular current based on the Einstein tensor, we discuss the issue of conserved charges and consider implications for matter coupled to gravity. The condition on the background geometry to allow asymptotic conserved charges for a current introduced by Kastor and Traschen is found and a number of other new aspects of this current are commented on. In particular we show that it vanishes for rank $(D-1)$ Killing-Yano tensors in $D$ dimensions.

1+21 pages, 1 table, no figures; version 2: clarifications added version 3: The d index raised in the middle formulae in (6.2) and (6.10). Makes the comments on (6.10) correct

References in corpus (8)

• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Killing-Yano equations and G-structures
• Do Killing-Yano tensors form a Lie Algebra?
• Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
• Killing-Yano Tensors of Order n-1
• Gravitational charges of transverse asymptotically AdS spacetimes
• Symmetries of $\mathcal{N}=(1,0)$ supergravity backgrounds in six dimensions
• Hidden Symmetries of the Dirac equation in curved spacetime

Cited by in corpus (10)

• Killing horizons and surface gravities for a well-behaved three-function generalisation of the Kerr spacetime
• Tensionless Strings and Killing(-Yano) Tensors
• Killing-Yano Cotton Currents
• Geometrical origin of the Kodama vector
• Geometry, conformal Killing-Yano tensors and conserved "currents"
• On the maximally symmetric vacua of generic Lovelock gravities
• Killing-Yano charges of asymptotically maximally symmetric black holes
• TCFHs, IIB warped AdS backgrounds and hidden symmetries
• TCFHs and hidden symmetries of type IIA AdS backgrounds
• The TCFHs of D=11 AdS backgrounds and hidden symmetries