On the Time Times Temperature Bound

TL;DR

This paper tests Hod's proposed lower bound on relaxation times in various spacetimes with known quasinormal frequencies, finding that some violate the bound, challenging its universality.

Contribution

It provides the first exact calculations of quasinormal frequencies in certain spacetimes to test Hod's bound, revealing violations in some cases.

Findings

Some spacetimes violate Hod's bound on relaxation times.

Exact quasinormal frequencies are computed for BTZ, de Sitter, and Nariai spacetimes.

The bound may not be universally applicable to all gravitational systems.

Abstract

Recently Hod proposes a lower bound on the relaxation time of a perturbed thermodynamic system. For gravitational systems this bound transforms into a condition on the fundamental quasinormal frequency. We test the bound in some spacetimes whose quasinormal frequencies are calculated exactly, as the three-dimensional BTZ black hole, the D-dimensional de Sitter spacetime, and the D-dimensional Nariai spacetime. We find that for some of these spacetimes their fundamental quasinormal frequencies do not satisfy the bound proposed by Hod.