Hidden symmetries and separability structures of Ovcharenko-Podolský and conformal-to-Carter spacetimes

Recently, a remarkable new class of spacetimes describing black holes immersed in a nonaligned electromagnetic field has been found. While still of type D, this class goes beyond the famous Plebański-Demiański family. Here we demonstrate that the whole class admits a hidden symmetry encoded in the nondegenerate conformal Killing-Yano 2-form. Interestingly, as a direct consequence of nonalignment of the electromagnetic field and contrary to the Plebański-Demiański class (where the field is aligned), such a symmetry no longer generates the full “tower of symmetries.” Despite this, it enables one to separate variables in massless Hamilton-Jacobi, conformal wave, and massless Dirac equations, as well as allows one to tackle massless vector and tensor perturbations. These results provide a useful mathematical tool for discussing numerous (astrophysical) applications to be described by these metrics. Moreover, as we shall show, the novel spacetimes provide an interesting test ground for studying the recently defined Penrose charges whose existence is intrinsically related to hidden rather than explicit symmetries.