Black Hole Quasinormal Mode Instability: Insights from the Pseudospectrum.

We will discuss the stability of the quasinormal mode spectrum
of black holes with an emphasis on asymptotically de Sitter geometries. To
capture the notion of spectral instability, we shall introduce and explain
the idea behind the pseudospectrum of non-self-adjoint operators. We shall
also highlight its implications on various aspects of black hole physics
including black hole spectroscopy. Our findings will be based on a study
of the spectrum and the pseudospectrum of asymptotically de Sitter black
holes carried out numerically using spectral methods in a hyperboloidal
foliation. Our analysis demonstrates how small deformations or
perturbations to the scattering potential may cause the quasinormal mode
frequencies to significantly deviate from their original values. We shall
compare our results with those obtained for asymptotically flat and
anti-de Sitter black holes. We shall also briefly highlight recent results
and open questions regarding the pseudospectrum of black holes.