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

TL;DR

This paper analytically investigates the relaxation spectrum of charged massive scalar fields around Reissner-Nordström black holes, demonstrating the universal relaxation bound and the quantum Schwinger discharge mechanism's role in preventing violations.

Contribution

It provides an analytical study of quasinormal modes showing the relaxation bound saturation and reveals how quantum pair production constrains system parameters.

Findings

The relaxation time saturates the universal bound in the large-coupling regime.

Quantum Schwinger discharge prevents violations of the relaxation bound.

Potential bound violations are excluded by quantum pair-production effects.

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 $qQ\ll M^2\mu^2/\hbar$.