Quasinormal modes of plane-symmetric black holes according to the AdS/CFT correspondence

TL;DR

This paper investigates the quasinormal modes of plane-symmetric anti-de Sitter black holes using the AdS/CFT correspondence, linking black hole perturbations to properties of a dual conformal field theory, and clarifies boundary conditions and gauge-invariant quantities.

Contribution

It unambiguously determines boundary conditions and gauge-invariant quantities for quasinormal modes of AdS black holes, revealing their hydrodynamic behavior and damping characteristics.

Findings

Hydrodynamic dispersion relations with diffusion, shear, and sound modes.

Presence of purely damped electromagnetic modes approaching Matsubara frequencies.

Different boundary conditions lead to revised quasinormal mode spectra.

Abstract

The electromagnetic and gravitational quasinormal spectra of $(3+1)$-dimensional plane-symmetric anti-de Sitter black holes are analyzed in the context of the AdS/CFT correspondence. According to such a correspondence, the electromagnetic and gravitational quasinormal frequencies of these black holes are associated respectively to the poles of retarded correlation functions of $R$-symmetry currents and stress-energy tensor in the holographically dual conformal field theory: the $(2+1)$-dimensional $\mathcal{N}=8$ super-Yang-Mills theory. The connection between AdS black holes and the corresponding field theory is used to unambiguously fix the boundary conditions that enter the proper definition of quasinormal modes. Such a procedure also helps one to decide, among the various different possibilities, what are the appropriate gauge-invariant quantities one should use in order to correctly describe the electromagnetic and gravitational blackhole perturbations. These choices imply in different dispersion relations for the quasinormal modes when compared to some of the results in the literature. In particular, the long-distance, low-frequency limit of dispersion relations presents the characteristic hydrodynamic behavior of a conformal field theory with the presence of diffusion, shear, and sound wave modes. There is also a family of purely damped electromagnetic modes which tend to the bosonic Matsubara frequencies in the long-wavelength regime.