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.
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Acknowledgments
It is a pleasure to thank Valentin Boyanov, Jose Luis Jaramillo, Rodrigo Panosso Macedo and Benjamin Withers for discussions. C.P. thanks the Princeton Center for Theoretical Science for hospitality during the programme “Workshop on Nonlinear Aspects of General Relativity”. C.P. and B.C. acknowledge support from a Royal Society — Science Foundation Ireland University Research Fellowship via grant URF/R1/211027. M.Z. acknowledges financial support by the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT — Fundação para a Ciência e a Tecnologia) — references UIDB/04106/2020 and UIDP/04106/2020 — as well as FCT projects 2022.00721.CEECIND, CERN/FIS-PAR/0027/2019, PTDC/FIS-AST/3041/2020, CERN/FIS-PAR/0024/2021 and 2022.04560.PTDC. This work has further been supported by the European Horizon Europe staff exchange (SE) programme HORIZON-MSCA-2021-SE-01 Grant No. NewFunFiCO-101086251.
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Cownden, B., Pantelidou, C. & Zilhão, M. The pseudospectra of black holes in AdS. J. High Energ. Phys. 2024, 202 (2024). https://doi.org/10.1007/JHEP05(2024)202
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DOI: https://doi.org/10.1007/JHEP05(2024)202