Killing-Yano forms and Killing tensors on a warped space

TL;DR

This paper develops criteria for lifting symmetries from base spaces to warped geometries, illustrating with examples including a new class of highly symmetric black hole solutions derived from Kerr-NUT-(A)dS spacetimes.

Contribution

It introduces explicit criteria for extending Killing and Killing-Yano symmetries to warped spaces and constructs new highly symmetric black hole solutions.

Findings

Criteria for symmetry lifting in warped geometries

Construction of new black hole solutions with inherited symmetries

Examples demonstrating the applicability of the criteria

Abstract

We formulate several criteria under which the symmetries associated with the Killing and Killing-Yano tensors on the base space can be lifted to the symmetries of the full warped geometry. The procedure is explicitly illustrated on several examples, providing new prototypes of spacetimes admitting such tensors. In particular, we study a warped product of two Kerr-NUT-(A)dS spacetimes and show that it gives rise to a new class of highly symmetric vacuum (with cosmological constant) black hole solutions that inherit many of the properties of the Kerr-NUT-(A)dS geometry.