Quasinormal modes and second order thermodynamic phase transition for Reissner-Nordstr\"om black hole

TL;DR

This paper investigates how quasinormal modes of Reissner-Nordström black holes encode information about second order thermodynamic phase transitions, revealing a spiral pattern in frequencies at the transition point.

Contribution

It demonstrates that quasinormal modes exhibit distinctive oscillatory behavior at the phase transition, linking dynamical properties to thermodynamic critical phenomena.

Findings

QNMs form spiral patterns at the phase transition point

Real and imaginary parts of frequencies oscillate with charge

QNMs can indicate the second order phase transition point

Abstract

The relation between the quasinormal modes (QNMs) and the second order thermodynamic phase transition (SOTPT) for the Reissner-Nordstr\"om (RN) black hole is studied. It is shown that the quasinormal frequencies of the RN black hole start to get a spiral-like shape in the complex $\omega$ plane and both the real and imaginary parts become the oscillatory functions of the charge if the real part of the quasinormal frequencies arrives at its maximum at the second order phase transition point of Davies for given overtone number and angular quantum number. That is to say, we can find out the SOTPT point from the QNMs of the RN black hole. The fact shows that the quasinormal frequencies carry the thermodynamical information of the RN black hole.