Quasibound states of a charged Dirac field around regular black holes

Abstract

We study quasibound states of a massive charged Dirac field on the Ayón-Beato--Garc\'ıa (ABG) regular black-hole background and determine how a charged regular geometry modifies the fermionic spectrum in the absence of superradiant amplification. We derive the separated Dirac equations, impose quasibound boundary conditions, and obtain the far-field trapping condition $Mμ^2-qQω_R>0$, whose weak-binding, same-sign limit is $Mμ>qQ$. The complex frequencies are computed in the frequency domain and checked against time-domain evolutions. Because ABG and Reissner--Nordström (RN) black holes have the same Newtonian and Coulomb tails, they share the leading hydrogenic real-frequency spectrum. Their differences appear in subleading shifts and, more prominently, in the damping rates. The ABG inner barrier can reduce the horizon flux, making some modes much longer lived than their RN counterparts. Within the explored parameter range, the Dirac quasibound modes remain damped: the regular charged geometry changes the lifetime of the fermionic cloud but does not produce a Dirac superradiant instability.