Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing

Abstract

From information theory and thermodynamic considerations a universal bound on the relaxation time \(\tau\) of a perturbed system is inferred, \(\tau \geq \hbar/\pi T\), where \(T\) is the system's temperature. We prove that black holes comply with the bound; in fact they actually {\it saturate} it. Thus, when judged by their relaxation properties, black holes are the most extreme objects in nature, having the maximum relaxation rate which is allowed by quantum theory.