Matrix method for perturbed black hole metric with discontinuity

Abstract

Abstract Recent studies based on the notion of black hole pseudospectrum indicated substantial instability of the fundamental and high-overtone quasinormal modes (QNMs). Besides its theoretical novelty, the details about the migration of the QNM spectrum due to specific perturbations may furnish valuable information on the properties of associated gravitational waves in a more realistic context. This work generalizes the matrix method for black hole QNMs to cope with a specific class of perturbations to the metric featured by discontinuity, which is known to be intimately connected with the QNM structural instability. In practice, the presence of discontinuity poses a difficulty so that many well-known approaches for QNMs cannot be straightforwardly applied. By comparing with other methods, we show that the modified matrix method is efficient, which can be used to solve for the low-lying modes with reasonable precision. Therefore, it might serve as an alternative gadget for relevant studies.