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arXiv · 1808.04077

The instability spectra of near-extremal Reissner-Nordstr\"om-de Sitter black holes

Shahar Hod
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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].

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Shahar Hod. 2018-08-13. The instability spectra of near-extremal Reissner-Nordstr\"om-de Sitter black holes. https://doi.org/10.1016/j.physletb.2018.09.039

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