Spectral (in)stability of quasinormal modes and strong cosmic censorship

Recent studies have shown that quasinormal modes suffer from spectral instabilities, a frailty of black holes that leads to disproportional migration of their spectra in the complex plane when black-hole effective potentials are modified by minuscule perturbations. Similar results have been found with the mathematical notion of the pseudospectrum which was recently introduced in gravitational physics. Environmental effects, such as the addition of a thin accretion disk or a matter shell, lead to a secondary bump that appears in the effective potential of black hole perturbations. Regardless of the environment's small contribution to the effective potential, its presence can completely destabilize the fundamental quasinormal mode and may potentially affect black hole spectroscopy. Here, we perform a comprehensive analysis of such phenomenon for Schwarzschild, Reissner-Nordstr\"om, Schwarzschild-de Sitter, and Reissner-Nordstr\"om-de Sitter black holes by considering the potential for a test scalar field with the addition of a tiny bump sufficiently away from the photon sphere. We find a qualitatively similar destabilization pattern for photon sphere, complex, scalar quasinormal modes in all cases, and a surprising spectral stability for dominant scalar, purely imaginary, de Sitter and near-extremal modes that belong to different families of the spectrum. For Reissner-Nordstr\"om-de Sitter black holes, we re-evaluate the validity of the strong cosmic censorship and find that the addition of a realistic bump in the effective potential cannot prevent its violation due to a combination of the spectral stability of dominant de Sitter and near-extremal modes for small cosmological constants and an ineffective migration of the photon sphere modes that dominate the late-time ringdown signal for sufficiently large cosmological constants.