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

TL;DR

This paper classifies five-dimensional Kaluza-Klein black hole metrics admitting a generalized Killing-Yano tensor with torsion, providing explicit forms and linking them to known supergravity solutions.

Contribution

It introduces a classification of five-dimensional metrics with generalized Killing-Yano tensors in the presence of torsion, including explicit local expressions and connections to supergravity black holes.

Findings

Metrics are classified into three types with explicit forms.

Some classes correspond to charged, rotating Kaluza-Klein black holes.

The study extends Killing-Yano symmetry concepts to torsionful geometries.

Abstract

Using a generalised Killing-Yano equation in the presence of torsion, spacetime metrics admitting a rank-2 generalised 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.