The pseudospectra of black holes in AdS
Abstract
We study the stability of quasinormal modes (QNMs) in electrically charged black brane spacetimes that asymptote to AdS by means of the pseudospectrum. Methodologically, we adopt ingoing Eddington-Finkelstein coordinates to cast QNMs in terms of a generalised eigenvalue problem involving a non-selfadjoint operator; this simplifies the computation significantly in comparison with previous results in the literature. Our analysis reveals spectral instability for (neutral) scalar as well as gravitoelectric perturbations. This indicates that the equilibration process of perturbed black branes is sensitive to external perturbations. Particular attention is given on the hydrodynamic modes, which are found to be the least unstable. In contrast with computations in hyperboloidal coordinates, we find that the pseudospectral contour lines cross to the upper half plane. This indicates the existence of pseudo-resonances as well as the possibility of transient instabilities. We also investigate the asymptotic structure of pseudospectral contour levels and we find remarkable universality across all sectors, persistent in the extremal limit.
Keywords
Cite
@article{arxiv.2312.08352,
title = {The pseudospectra of black holes in AdS},
author = {Brad Cownden and Christiana Pantelidou and Miguel Zilhão},
journal= {arXiv preprint arXiv:2312.08352},
year = {2024}
}
Comments
38 pages, 13 figures V3: Updated to match the published version in JHEP. V4: updated plots for scalar field pseudospectra to reflect correction in numerics -- no change in conclusions. Correction of factor in equation for the energy of the master scalar