Generalized hidden symmetries and the Kerr-Sen black hole

TL;DR

This paper explores generalized Killing-Yano tensors with torsion, revealing their role in integrability and separability of equations in Kerr-Sen black hole spacetimes across dimensions.

Contribution

It introduces the concept of generalized Killing-Yano tensors with torsion and demonstrates their existence in Kerr-Sen black holes, linking them to integrability and separability.

Findings

Existence of a generalized closed conformal Killing-Yano 2-form in Kerr-Sen spacetime

This form ensures complete integrability of geodesic motion

It allows for the separability of scalar and Dirac equations

Abstract

We elaborate on basic properties of generalized Killing-Yano tensors which naturally extend Killing-Yano symmetry in the presence of skew-symmetric torsion. In particular, we discuss their relationship to Killing tensors and the separability of various field equations. We further demonstrate that the Kerr-Sen black hole spacetime of heterotic string theory, as well as its generalization to all dimensions, possesses a generalized closed conformal Killing-Yano 2-form with respect to a torsion identified with the 3-form occuring naturally in the theory. Such a 2-form is responsible for complete integrability of geodesic motion as well as for separability of the scalar and Dirac equations in these spacetimes.