Charged Dirac perturbations on Reissner-Nordstr\"om black holes in a cavity: quasinormal modes with Robin boundary conditions

TL;DR

This paper studies charged Dirac field perturbations around Reissner-Nordström black holes confined in a cavity, analyzing quasinormal modes with Robin boundary conditions, revealing spectral symmetries and novel decay behaviors influenced by charge interactions.

Contribution

It derives and computes charged Dirac quasinormal spectra with Robin boundary conditions, uncovering spectral symmetries and anomalous decay patterns near black hole horizons.

Findings

Spectral symmetry between two boundary conditions.

Asymptotic spectra near horizon depend on charge and overtone number.

Large charge coupling causes excited modes to decay slower than fundamental modes.

Abstract

We investigate charged Dirac quasinormal spectra on Reissner-Nordstr\"om black holes in a mirror-like cavity. For this purpose, we first derive charged Dirac equations, and \textit{two} sets of Robin boundary conditions following the vanishing energy flux principle. The Dirac spectra are then computed both analytically and numerically. Our results reveal a symmetry hidden in the Dirac spectra between two boundary conditions. Moreover, when the cavity is placed close to the event horizon $r_+$, we identify that, in the neutral background the Dirac spectra asymptote to $-(3/8+N/2)i$ [$-(1/8+N/2)i$] for the first [second] boundary condition; while in the charged background the real part of charged Dirac spectra asymptote to $qQ/r_+$ for both boundary conditions; where $N$ is the overtone number, $q$ and $Q$ are charges for the field and for the background. In particular, we uncover a striking anomalous decay pattern, $i.e.$ the excited modes decay \textit{slower} than the fundamental mode, when the charge coupling $qQ$ is large. Our results further illustrate the robustness of vanishing energy flux principle, which are applicable not only to anti-de Sitter black holes but also to black holes in a cavity.