Charged Dirac perturbations on Reissner-Nordström black holes in a cavity: quasinormal modes with Robin boundary conditions

We investigate charged Dirac quasinormal spectra on Reissner-Nordström black holes in a mirror-like cavity. For this purpose, we first derive charged Dirac equations, and $\mathit{\text{two}}$ 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 $-(3\mathrm{/}8+N\mathrm{/}2)i$ [$-(1\mathrm{/}8+N\mathrm{/}2)i$] for the first [second] boundary condition; while in the charged background the real part of charged Dirac spectra asymptote to $qQ\mathrm{/}{r}_{+}$ 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, $i\mathrm{.}e\mathrm{.}$ the excited modes decay $\mathit{\text{slower}}$ 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.