Quasinormal modes and thermodynamic phase transitions

TL;DR

This paper investigates the proposed link between quasinormal modes of black holes and their thermodynamic phase transitions, finding that the connection may be coincidental and not universally applicable across different black hole metrics.

Contribution

The study critically examines previous claims of a direct relation between black hole perturbations and thermodynamic phase transitions, showing the lack of a straightforward generalization.

Findings

The proposed correlation is likely a numerical coincidence.

The relation does not easily extend to Kerr or Schwarzschild (anti-)de Sitter black holes.

A non-trivial relation between dynamical and thermodynamical properties remains possible.

Abstract

It has recently been suggested that scalar, Dirac and Rarita-Schwinger perturbations are related to thermodynamic phase transitions of charged (Reissner-Nordstr\"om) black holes. In this note we show that this result is probably a numerical coincidence, and that the conjectured correspondence does not straightforwardly generalize to other metrics, such as Kerr or Schwarzschild (anti-)de Sitter. Our calculations do not rule out a relation between dynamical and thermodynamical properties of black holes, but they suggest that such a relation is non-trivial.