New relations involving the Riemann, Ricci and Einstein tensors that have to hold for a given geometry to admit Killing–Yano tensors (KYTs) are described. These relations are then used to introduce novel conserved ‘currents’ involving such KYTs. 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) KYTs in D dimensions.

描述了涉及黎曼张量、里奇张量和爱因斯坦张量的新关系，这些张量对于给定的几何形状必须成立，以承认 Killing-Yano 张量 (KYT)。然后使用这些关系来引入涉及此类 KYT 的新的保守“电流”。对于基于爱因斯坦张量的特定电流，我们讨论守恒电荷问题并考虑对与重力耦合的物质的影响。背景几何条件允许由 Kastor 和 Traschen 引入的电流的渐近守恒电荷被发现，并且对该电流的许多其他新方面进行了评论。特别地，我们表明它在D维中的等级 ( D − 1) KYT 中消失。