Slowly decaying resonances of charged massive scalar fields in the Reissner-Nordström black-hole spacetime

Abstract

We determine the characteristic timescales associated with the linearized relaxation dynamics of the composed Reissner-Nordström-black-hole-charged-massive-scalar-field system. To that end, the quasinormal resonant frequencies $\{{\omega }_n(\mu ,q,M,Q){\}}_{n=0}^{n=\infty }$ which characterize the dynamics of a charged scalar field of mass $\mu$ and charge coupling constant $q$ in the charged Reissner-Nordström black-hole spacetime of mass $M$ and electric charge $Q$ are determined {\it analytically} in the eikonal regime $1\ll M\mu <qQ$. Interestingly, we find that, for a given value of the dimensionless black-hole electric charge $Q/M$, the imaginary part of the resonant oscillation frequency is a monotonically {\it decreasing} function of the dimensionless ratio $\mu /q$. In particular, it is shown that the quasinormal resonance spectrum is characterized by the asymptotic behavior $\Im \omega \to 0$ in the limiting case $M\mu \to qQ$. This intriguing finding implies that the composed Reissner-Nordström-black-hole-charged-massive-scalar-field system is characterized by extremely long relaxation times ${\tau }_{\text{relax}}\equiv 1/\Im \omega \to \infty$ in the $M\mu /qQ\to 1^{-}$ limit.

8 pages

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• Stationary scalar clouds around a BTZ black hole
• The longlived charged massive scalar field in the higher-dimensional Reissner--Nordström spacetime
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• Stability and phase transition of rotating Kaluza-Klein black holes
• Gravitational atoms in the braneworld scenario
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• Traversable wormholes in bi-metric gravity
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