Slowly decaying resonances of charged massive scalar fields in the Reissner-Nordstr\"om black-hole spacetime

TL;DR

This paper analytically investigates the quasinormal modes of charged massive scalar fields around Reissner-Nordström black holes, revealing that relaxation times become extremely long as the field's mass-to-charge ratio approaches a critical value.

Contribution

It provides an analytical determination of quasinormal frequencies in the eikonal regime, uncovering the long relaxation times near the threshold where the scalar field mass-to-charge ratio approaches the black hole charge-to-mass ratio.

Findings

Imaginary part of frequencies decreases monotonically with increasing field mass-to-charge ratio.

Quasinormal modes tend to zero imaginary part as the mass-to-charge ratio approaches the critical value.

Relaxation times diverge, indicating extremely slow decay of perturbations near the threshold.

Abstract

We determine the characteristic timescales associated with the linearized relaxation dynamics of the composed Reissner-Nordstr\"om-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-Nordstr\"om 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 $\Im\omega\to0$ in the limiting case $M\mu\to qQ$. This intriguing finding implies that the composed Reissner-Nordstr\"om-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.