Killing–Yano symmetry of Kaluza–Klein black holes in five dimensions

Abstract

Using a generalized Killing–Yano equation in the presence of torsion, spacetime metrics admitting a rank-2 generalized Killing–Yano tensor are investigated in five dimensions under the assumption that its eigenvector associated with the zero eigenvalue is a Killing vector field. It is shown that such metrics are classified into three types and the corresponding local expressions are given explicitly. It is also shown that they cover some classes of charged, rotating Kaluza–Klein black hole solutions of minimal supergravity and Abelian heterotic supergravity.