Preserving Kerr symmetries in deformed spacetimes

We present a novel approach in constructing deviations of the Kerr spacetime whereas the symmetries can be preserved. The method was applied trivially in all known classical black-hole spacetimes tested, while providing the possibility of testing and inventing deformations of Kerr in a quick and innovative way. The methodology is based on earlier work by Benenti and Francaviglia (1979 Gen. Relativ. Gravit . 10 79) on separability of geodesic equations while we exploited the elegant properties of Yano tensor in order to provide an additional way of getting the Carter constant.