Destabilizing the Fundamental Mode of Black Holes: The Elephant and the Flea

Mark Ho-Yeuk Cheung, Kyriakos Destounis, Rodrigo Panosso Macedo, Emanuele Berti, and Vitor Cardoso

Phys. Rev. Lett. 128, 111103 – Published 18 March 2022

Abstract

Recent work applying the notion of pseudospectrum to gravitational physics showed that the quasinormal mode spectrum of black holes is unstable, with the possible exception of the longest-lived (fundamental) mode. The fundamental mode dominates the expected signal in gravitational wave astronomy, and there is no reason why it should have privileged status. We compute the quasinormal mode spectrum of two model problems where the Schwarzschild potential is perturbed by a small “bump” consisting of either a Pöschl-Teller potential or a Gaussian, and we show that the fundamental mode is destabilized under generic perturbations. We present phase diagrams and study a simple double-barrier toy problem to clarify the conditions under which the spectral instability occurs.

Received 18 November 2021
Revised 7 January 2022
Accepted 23 February 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.111103

Physics Subject Headings (PhySH)

Classical black holes General relativity

Perturbation theory

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Mark Ho-Yeuk Cheung ¹, Kyriakos Destounis ², Rodrigo Panosso Macedo ^3,4, Emanuele Berti ¹, and Vitor Cardoso ^5,3

¹Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
²Theoretical Astrophysics, IAAT, University of Tübingen, 72076 Tübingen, Germany
³CENTRA, Departamento de Física, Instituto Superior Técnico–IST, Universidade de Lisboa–UL, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal
⁴STAG Research Centre, University of Southampton, University Road, SO17 1BJ Southampton, United Kingdom
⁵Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark