On the Relationship Between Killing-Yano Tensors and Electromagnetic Fields on Curved Spaces

The existence of skew symmetric Killing-Yano (KY) tensors of order 2 has been investigated on curved spaces. The integrability conditions of KY tensor including Carter's algebraic relation of symmetric tensor with electromagnetic field have been transcribed in Newman-Penrose formalism. The KY bivectors are classified according to their nullity in electrovac space-times. It is shown that the non-null (or null) electromagnetic field implies to the existence of non-null (or null) KY tensor. Thus Collinson's theorems on the existence of KY tensors on vacuum space-times have been generalized on electrovac space-times. Chandrasekhar's theorem on vacuum type D space-times has also been generalized on the existence of non-null KY tensor on electrovac type D or non-vacuum type D space-time filled with dust. All theorems presented here have been strengthened by giving examples for known space-times. It is also shown that most of KY tensors discussed here are eigen-KY-bivectors of the respective curvature tensors.