Quasinormal modes of Schwarzschild-de Sitter black holes in semi-open systems

TL;DR

This paper investigates how adding a semi-open boundary around Schwarzschild-de Sitter black holes affects their quasinormal modes, greybody factors, and exceptional points, revealing new behaviors and mode interactions.

Contribution

It introduces a semi-open system model with a reflective wall, analyzing its impact on QNM spectra, greybody factors, and the emergence of exceptional points, which is a novel approach in black hole perturbation studies.

Findings

Identification of three distinct QNM behaviors with increasing reflectivity

Observation of strong oscillations in greybody factors controlled by the wall distance

Discovery of a second-order exceptional point and mode exchange phenomena

Abstract

We study perturbations of Schwarzschild-de Sitter black holes in semi-open systems by using the Heun functions. For the semi-open system, a partially reflective wall is added around the event horizon. Three aspects of this model are investigated, namely the quasinormal mode (QNM) spectra, the greybody factor (GF), and the exceptional point (EP). For the QNM aspect, we identify three distinct behaviors as the frequency-independent reflectivity $\mathcal{K}$ increasing. The first-type modes approach the real axis and form long-lived quasi-bound states. The second-type modes move toward but do not reach the real axis and retain a finite decay rate. The third-type modes eventually lie on the imaginary axis becoming purely decaying modes. For the GF aspect, GFs exhibit strong oscillations controlled by the distance between the potential and the reflective wall with a real constant reflectivity. In contrast, a Boltzmann-type reflectivity produces only small corrections. Finally, by promoting $\mathcal{K}$ to a complex parameter, the modified boundary conditions give rise to a second-order EP. Parameterizing the vicinity of such EP, we observe the mode exchange phenomenon, and the deviation of spectra scale with the square root of the deviation of the parameter, as predicted by a Puiseux series expansion.