Pseudospectra of complex momentum modes

TL;DR

This paper explores the stability and pseudospectra of complex momentum modes in asymptotically anti-de Sitter black holes, revealing their distinct properties compared to quasinormal modes and demonstrating their stability under perturbations.

Contribution

It introduces the study of complex momentum mode pseudospectra in AdS black holes, highlighting differences from quasinormal modes and analyzing their stability and numerical properties.

Findings

Pseudospectra of complex momentum modes differ significantly from quasinormal modes.

The resolvent for these modes is well-defined with rapid numerical convergence.

Low-frequency modes are stable and resistant to destabilization by local perturbations.

Abstract

We initiate the study of stability and pseudospectra of complex momentum modes of asymptotically anti-de Sitter black holes. Similar to quasinormal modes, these can be defined as the poles of the holographic Green's function, albeit for real frequency and complex momentum. Their pseudospectra are in stark contrast to the pseudospectra of quasinormal modes of AdS black holes. Contrary to the case of quasinormal mode pseudospectra, the resolvent is well-defined, and the numerical approximation shows fast convergence. At zero frequency, complex momentum modes are stable normal modes of a Hermitian operator. Even for large frequencies, they show only comparatively mild spectral instability. We also find that local potential perturbations cannot destabilize the lowest complex momentum mode.