Universality in the relaxation dynamics of the composed black-hole-charged-massive-scalar-field system: The role of quantum Schwinger discharge

Abstract

The quasinormal resonance spectrum $\{\omega_n(\mu,q,M,Q)\}_{n=0}^{n=\infty}$ of charged massive scalar fields in the charged Reissner-Nordstr\"om black-hole spacetime is studied {\it analytically} in the large-coupling regime $qQ\gg M\mu$ (here $\{\mu, q\}$ are respectively the mass and charge coupling constant of the field, and $\{M,Q\}$ are respectively the mass and electric charge of the black hole). This physical system provides a striking illustration for the validity of the universal relaxation bound $\tau \times T \geq \hbar/\pi$ in black-hole physics (here $\tau\equiv 1/\Im\omega_0$ is the characteristic relaxation time of the composed black-hole-scalar-field system, and $T$ is the Bekenstein-Hawking temperature of the black hole). In particular, it is shown that the relaxation dynamics of charged massive scalar fields in the charged Reissner-Nordstr\"om black-hole spacetime may {\it saturate} this quantum time-times-temperature inequality. Interestingly, we prove that potential violations of the bound by light scalar fields are excluded by the Schwinger-type pair-production mechanism (a vacuum polarization effect), a {\it quantum} phenomenon which restricts the physical parameters of the composed black-hole-charged-field system to the regime $qQ\ll M^2\mu^2/\hbar$.