Résumé

In this talk we explore the issue of black hole quasi-normal mode (QNM) instability.  Specifically, by adopting a hyperboloidal approach to QNMs we cast the QNM problem as an eigenvalue problem for a non-selfadjoint operator. Such operators suffer potentially of instabilities in their spectrum and this point is addressed by specific tools in  non-selfadjoint spectral theory, among them the notion of pseudospectrum.  At an exploratory stage prior to the full analytical study,  we adopt here a numerical methodology based on pseudospectral methods.  After studying the Pöschl-Teller potential as a toy model already containing the main features of the discussion, we address the black hole Schwarzschild case. As a result of our analysis, we find strong support to claim: i) the stability of the slowest decaying mode, and ii) the instability of all QNM overtones. We will conclude with a discussion of the potential implications in astrophysics and fundamental physics.

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