Hidden Symmetries and Higher Dimensional Rotating Black Holes

A standard approach to probing the dynamics of a physical system is to expose it to an external perturbation—such as an incident wave—and analyze its response after the interaction. Mathematically, this procedure is formulated in terms of differential equations governing the evolution of the perturbation. In the context of black hole physics, an analogous strategy can be employed by studying the response of the event horizon to external perturbations. The differential equations describing these interactions are often invariant under nontrivial transformations, revealing hidden symmetries that help explain distinctive features of higher-dimensional black holes. By exploiting these hidden symmetries in the equations of motion, we obtain several key results. First, we provide evidence for the existence of a two-dimensional holographic conformal field theory dual associated with five-dimensional rotating black rings and black strings. Second, we investigate whether higher-dimensional rotating black holes exhibit rigidity under tidal deformations and find that, in general, they do not. Third, we show that the perturbation equations under consideration belong to the broader class of generalized Heun equations. We introduce a novel transformation that simplifies these equations and enables the construction of their full analytic solutions. As an application, we use these results to compute tidal response coefficients, demonstrating the non-rigidity of the seven-dimensional Myers–Perry black hole.