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

TL;DR

This paper explores dualities in four-dimensional black hole spacetimes, their algebraic structures, and implications for holographic thermal CFTs, revealing constraints on spectral properties and quasinormal modes.

Contribution

It introduces a geometrical framework for black hole dualities, connects algebraic structures to spectral dualities in holography, and provides explicit constructions and numerical evidence.

Findings

Dualities impose constraints on thermal spectra of correlators.

Spectral duality relates longitudinal and transverse quasinormal modes.

Numerical results support the spectral duality relation in holographic CFTs.

Abstract

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.