Massive charged Dirac fields around Reissner-Nordström black holes: Quasibound states and long-lived modes

Abstract

The behavior of a massive charged test Dirac field in the background of a Reissner-Nordström black hole is investigated. Especially, we obtain the frequencies of quasibound states by solving the Dirac equation numerically both in time and frequency domain. Our results suggest that although the absence of superradiance excludes the existence of stationary solutions for massive Dirac fields, it is still possible to find arbitrarily long-lived solutions.the intermediate states between the decaying and superradiantly growing ones [23][24][25][26][27][28]. It is not possible to find such stationary clouds for Dirac fields in BH spacetimes due to the absence of superradiance [29,30]. However, for Dirac fields around a rapidly rotating Kerr BH, the decay rate of the co-rotating mode is suppressed, so long as the real part of the bound state frequency obeys a 'superradiant'-like condition [8].

Quasinormal modes of a charged spherical black hole with scalar hair for scalar and Dirac perturbations

“…In the asymptotic limits of the tortoise coordinate equation (36) can be solved analytically with the QNM boundary conditions yielding…”

Dirac clouds around dilatonic black holes

“…More interestingly, when µM ≪ 1, the real bound state we have found has a hydrogen-like spectrum [14,15]…”

Scattering and absorption of a scalar field impinging on a charged black hole in the Einstein-Maxwell-dilaton theory

“…There were also numerical evidences that RN black hole supporting the superradiant instability against massive charged perturbation of zero spin contained in a cavity; in fact, the final state of such configuration corresponds to a hairy black hole plus a boson condensate [76]. Besides, the case of charged RN impinged by a massive charged Dirac field was estudied by Huang et al [77], excluding the superradiance instability. For a massive charged boson field within a Kerr-Newman background, the superradiant instability would seem more favorable in comparison to a boson field around a Kerr black hole [78].…”