Quasinormal Modes of Charged Fermions and Phase Transition of Black Holes

TL;DR

This paper investigates the quasinormal modes of charged fermions in a charged black hole spacetime, revealing conditions under which black hole instability and phase transitions occur, interpreted as superconducting transitions via AdS/CFT correspondence.

Contribution

It provides new insights into the stability and phase transition behavior of charged fermions around black holes, especially regarding the influence of fermion coupling strength and charge.

Findings

Imaginary part of quasinormal frequency becomes positive below a critical temperature.

Stronger fermion-electric field coupling raises the critical temperature.

Neutral fermions do not induce black hole instability or phase transition.

Abstract

We study the quasinormal modes of massless charged fermions in a Reissner-Nordstrom-anti-de Sitter black hole spacetime. In the probe limit, we find that the imaginary part of quasinormal frequency will become positive when the temperature of the black hole is below a critical value. This indicates an instability of the black hole occurs and a phase transition happens. In the AdS/CFT correspondence, this transition can be viewed as a superconducting phase transition and the bulk fermion is regarded as the order parameter. When the coupling of the fermions and the background electric field becomes stronger, the critical temperature of the phase transition becomes higher. If the interaction between the fermion and the electric field can be ignored, namely in the case of a neutral fermion, the imaginary part of the quasinormal modes is always negative, which indicates that the black hole is stable and no phase transition occurs.