Pseudospectrum and Black Hole Quasinormal Mode Instability

We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means a pseudospectrum analysis. The construction Schwarzschild QNM reveals following: (i) slowest-decaying under perturbations respecting asymptotic structure, reassessing instability fundamental discussed Nollert [H. P. Nollert, About Significance Quasinormal Modes Black Holes, Phys. Rev. D 53, 4397 (1996)] as an "infrared" effect; (ii) all overtones small-scale ("ultraviolet") sufficiently high frequency, which migrate towards universal branches along pseudospectra boundaries, shedding light on Nollert's pioneer work and Price's analysis R. H. Price, Quantifying Excitations Mode Systems, J. Math. (N.Y.) 40, 980 (1999)]. Methodologically, compactified hyperboloidal approach to QNMs is adopted cast terms spectral problem non-self-adjoint operator. In this setting, (in)stability naturally addressed through notion that we construct numerically via Chebyshev methods foster gravitational physics. After illustrating with P\"oschl-Teller potential, address case, where (in)stabilities are physically relevant context spectroscopy gravitational-wave physics and, conceivably, probes into high-frequency spacetime fluctuations at Planck scale.