The instability spectra of near-extremal Reissner-Nordström-de Sitter black holes (1808.04077v2)

Abstract: The linearized dynamics of charged massive scalar fields in the near-extremal charged Reissner-Nordstr\"om-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 {\it unstable} (exponentially growing in time) complex resonant modes. Using a WKB analysis in the eikonal large-mass regime $M\mu\gg1$, we provide a remarkably compact analytical formula for the quasinormal resonant spectrum ${\omega_n(M,Q,\Lambda,\mu,q)}_{n=0}^{n=\infty}$ which characterizes the unstable modes of the composed RNdS-black-hole-charged-massive-scalar-field system [here ${M,Q,\Lambda}$ are respectively the mass, electric charge, and cosmological constant of the black-hole spacetime, and ${\mu,q}$ are the proper mass and charge coupling constant of the linearized field].