Abstract

In recent years there has been considerable progress in the study of properties of the higher-dimensional Kerr-NUT-(Anti) de Sitter black hole spacetimes. This progress builds on the discovery that the spacetimes admit a non-degenerate closed conformal Killing-Yano (CKY) 2-form which generates the hidden symmetries of the spacetimes. In this talk we first generalize the Kerr-NUT-(Anti)de Sitter spacetime by removing the non-degenerate condition, and obtain a complete local classification of spacetimes admitting a closed CKY 2 -form. The metrics are explicitly written as Kaluza-Klein metrics on the bundles over the Kahler manifolds whose fibers are Kerr-NUT-de Sitter spacetimes. Next we construct compact Einstein manifolds with a closed CKY 2 -form from the generalized Euclidean Kerr-NUT-de Sitter spacetimes. These arise in particular on sphere bundles over Einstein-Kahler manifolds with positive first Chern class, which have been studied recently by Hashimoto-Sakaguchi-Yasui, Gibbons-Lu-Page-Pope, Lu-Page-Pope et.al. Our construction provides a unifying framework for these works, and at the same time leads to the much larger class of new compact Einstein manifolds, including Sasaki-Einstein manifolds.