Dirac quasinormal frequencies of Reissner-Nordstr\"om black hole in Anti-de Sitter spacetime

TL;DR

This paper investigates the Dirac quasinormal modes of Reissner-Nordström black holes in Anti-de Sitter spacetime, revealing linear relations with Hawking temperature and charge, and analyzing their implications via AdS/CFT correspondence.

Contribution

It provides new insights into how black hole charge affects Dirac quasinormal frequencies and their spacing, with implications for dual conformal field theories.

Findings

Quasinormal frequencies are linear functions of Hawking temperature for large black holes.

Frequency spacing becomes evenly spaced at high overtone numbers.

Charge influences the real and imaginary parts of frequencies and their relation to angular quantum number.

Abstract

The quasinormal modes (QNMs) of Dirac field perturbations of a Reissner-Nordstr\"om black hole in an asymptotically Anti-de Sitter spacetime are investigated. We find that both the real and imaginary parts of the fundamental quasinormal frequencies for large black holes are the linear functions of the Hawking temperature, and the slope of the lines for the real parts decreases while that for the magnitude of the imaginary parts increases as the black hole charge increases. According to the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, the fact shows that different charge presents different time scale in three-dimensional CFT. Another interesting result is that the quasinormal frequencies become evenly spaced for high overtone number, and in the spacing expressions the real part decreases while the magnitude of the imaginary part increases as the charge increases. We also study the relation between quasinormal frequencies and angular quantum number and find that the real part increases while the magnitude of the imaginary part decreases as the angular quantum number increases.