On the time times temperature bound

Recently Hod proposed 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.