The instability spectra of near-extremal Reissner-Nordström-de Sitter black holes

The linearized dynamics of charged massive scalar fields in the near-extremal charged Reissner-Nordström-de Sitter (RNdS) black-hole spacetime is studied analytically. Interestingly, it is proved that the non-asymptotically flat charged black-hole-field system is characterized by unstable (exponentially growing in time) complex resonant modes. Using a WKB analysis in the eikonal large-mass regime Mμ≫1, we provide a remarkably compact analytical formula for the quasinormal resonant spectrum {ωn(M,Q,Λ,μ,q)}n=0n=∞ which characterizes the unstable modes of the composed RNdS-black-hole-charged-massive-scalar-field system [here {M,Q,Λ} are respectively the mass, electric charge, and cosmological constant of the black-hole spacetime, and {μ,q} are the proper mass and charge coupling constant of the linearized field].