Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime

Abstract

In our previous paper (arXiv:0805.0838[hep-th]), we proposed a generalization of the Kerr-NUT-de Sitter spacetimes and stated that they are the most general spacetimes admitting a rank-2 closed conformal Killing-Yano (CKY) tensor. In this paper, we prove this statement. When the eigenvalues of the CKY tensor are non-degenerate, the original Kerr-NUT-de Sitter spacetimes are the only spacetimes admitting such a non-degenerate CKY tensor.