  Quasinormal modes and frequencies are the eigenvectors and eigenvalues of a
non-Hermitian differential operator. They hold crucial significance in the
physics of black holes. The analysis of quasinormal modes of black holes in
asymptotically Anti-de Sitter geometries plays also a key role in the study of
strongly coupled quantum many-body systems via gauge/gravity duality. In
contrast to normal Sturm-Liouville operators, the eigenvalues of non-Hermitian
(and non-normal) operators generally exhibit instability under small
perturbations. This research focuses on the stability analysis of quasinormal
frequencies pertaining to asymptotically planar AdS black holes, employing
pseudospectrum analysis. Specifically, we concentrate on the pseudospectra of
scalar and transverse gauge fields, shedding light on their relevance within
the framework of gauge/gravity duality.
