Duality and four-dimensional black holes: Gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs

The physics of gravitational waves and other classical fields on specifically four-dimensional backgrounds of black holes exhibits electric-magnetic-like dualities. In this paper, we discuss the structure of such dualities in terms of geometrical quantities with a physically intuitive interpretation. In turn, we explain the interplay between the algebraic structure of black hole spacetimes and their associated dualities. For large classes of black hole geometries, explicit constructions are presented. We then use these results and apply them to the holographic study of three-dimensional conformal field theories (CFTs), discussing how such dualities place stringent constraints on the thermal spectra of correlators. In particular, the dualities enforce the recently developed spectral duality relation along with a multitude of implications for the physics of thermal CFTs. A number of numerical results supporting our conclusions is also presented, including a demonstration of how the longitudinal spectrum of quasinormal modes determines the transverse spectrum, and vice versa.