Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion

TL;DR

This paper analytically computes quasinormal mode frequencies of various (Anti-)de Sitter black holes using a 1/D expansion, revealing insights into their stability, hydrodynamic behavior, and limitations of the expansion.

Contribution

It provides higher-order analytical calculations of quasinormal modes for (Anti-)de Sitter black holes using the inverse-dimensional expansion, including unstable modes and hydrodynamic limits.

Findings

Calculated quasinormal frequencies for different horizon geometries.

Extended the accuracy of Gregory-Laflamme instability frequencies.

Compared AdS black brane modes with hydrodynamic expansion results.

Abstract

We use the inverse-dimensional expansion to compute analytically the frequencies of a set of quasinormal modes of static black holes of Einstein-(Anti-)de Sitter gravity, including the cases of spherical, planar or hyperbolic horizons. The modes we study are decoupled modes localized in the near-horizon region, which are the ones that capture physics peculiar to each black hole (such as their instabilities), and which in large black holes contain hydrodynamic behavior. Our results also give the unstable Gregory-Laflamme frequencies of Ricci-flat black branes to two orders higher in 1/D than previous calculations. We discuss the limits on the accuracy of these results due to the asymptotic but not convergent character of the 1/D expansion, which is due to the violation of the decoupling condition at finite D. Finally, we compare the frequencies for AdS black branes to calculations in the hydrodynamic expansion in powers of the momentum k. Our results extend up to k^9 for the sound mode and to k^8 for the shear mode.