Hidden symmetries and separability structures of Ovcharenko-Podolsk\'y and conformal-to-Carter spacetimes

TL;DR

This paper explores a new class of black hole spacetimes with hidden symmetries, enabling variable separation in key equations and offering insights into astrophysical phenomena and Penrose charges.

Contribution

It demonstrates the existence of hidden conformal symmetries in a novel class of non-aligned electromagnetic black hole spacetimes, extending the understanding beyond Plebański--Demiański solutions.

Findings

Hidden conformal Killing--Yano 2-form exists in these spacetimes.

Separation of variables achieved in massless field equations.

Provides a new testing ground for Penrose charges.

Abstract

Recently, a remarkable new class of spacetimes describing black holes immersed in a non-aligned electromagnetic field has been found. While still of type D, this class goes beyond the famous Pleba\'nski--Demia\'nski family. Here we demonstrate that the whole class admits a hidden symmetry encoded in the non-degenerate conformal Killing--Yano 2-form. Interestingly, as a direct consequence of non-alignment of the electromagnetic field and contrary to the Pleba\'nski--Demia\'nski 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.