Resonance spectra of caged black holes

TL;DR

This paper analytically investigates the resonance spectra of scalar fields confined near black holes, revealing a simple formula for the fundamental quasinormal modes that dominate late-time dynamics.

Contribution

It provides an analytical expression for the fundamental quasinormal resonances of caged Reissner-Nordström black holes, extending understanding of confined black-hole-field systems.

Findings

Derived a simple analytical formula for fundamental quasinormal modes.

Resonance frequencies are proportional to black hole temperature.

Results applicable to near-horizon confining mirror configurations.

Abstract

Recent numerical studies of the coupled Einstein-Klein-Gordon system in a cavity have provided compelling evidence that {\it confined} scalar fields generically collapse to form black holes. Motivated by this intriguing discovery, we here use analytical tools in order to study the characteristic resonance spectra of the confined fields. These discrete resonant frequencies are expected to dominate the late-time dynamics of the coupled black-hole-field-cage system. We consider caged Reissner-Nordstr\"om black holes whose confining mirrors are placed in the near-horizon region $x_{\text{m}}\equiv (r_{\text{m}}-r_+)/r_+\ll\tau\equiv (r_+-r_-)/r_+$ (here $r_{\text{m}}$ is the radius of the confining mirror and $r_{\pm}$ are the radii of the black-hole horizons). We obtain a simple analytical expression for the fundamental quasinormal resonances of the coupled black-hole-field-cage system: $\omega_n=-i2\pi T_{\text{BH}}\cdot n[1+O(x^n_{\text{m}}/\tau^n)]$, where $T_{\text{BH}}$ is the temperature of the caged black hole and $n=1,2,3,...$ is the resonance parameter.