Pseudospectrum of Reissner-Nordstr\"om black holes: quasinormal mode instability and universality

TL;DR

This paper investigates the pseudospectrum of Reissner-Nordström black holes, revealing spectral instability of quasinormal modes and uncovering gauge-independent features and a conformal duality responsible for isospectrality.

Contribution

It extends pseudospectral analysis to Reissner-Nordström black holes, demonstrating spectral instability and gauge independence, and uncovers a conformal duality causing isospectrality.

Findings

Spectral instability of scalar and gravitoelectric modes in extremal and subextremal black holes.

Pseudospectral contours exhibit gauge-independent asymptotic structure.

Extremal Reissner-Nordström black holes show strong isospectrality between gravitational and electromagnetic modes.

Abstract

Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational spectroscopy, so it is critical to understand if the quasinormal mode spectrum is stable against perturbations. It was recently shown that the pseudospectrum can shed light on the spectral stability of black hole quasinormal modes. We study the pseudospectrum of Reissner-Nordstr\"om spacetimes and we find a spectral instability of scalar and gravitoelectric quasinormal modes in subextremal and extremal black holes, extending similar findings for the Schwarzschild spacetime. The asymptotic structure of pseudospectral contour levels is the same for scalar and gravitoelectric perturbations. By making different gauge choices in the hyperboloidal slicing of the spacetime, we find that the broad features of the pseudospectra are remarkably gauge-independent. The gravitational-led and electromagnetic-led quasinormal modes of extremal Reissner-Nordstr\"om black holes exhibit "strong" isospectrality: not only their spectrum coincides, but the whole pseudospectrum is the same for both classes of perturbations. We observe that a conformal duality between the extremal horizon and spacetime boundaries at infinity is responsible for such "strong" isospectrality property.