Quasinormal modes of charged dilaton black holes and their entropy spectra

TL;DR

This paper investigates the quasinormal modes of charged dilaton black holes derived from string theory, revealing that their quantum entropy and area spectra are equally spaced and independent of the dilaton parameter, with a specific constant value.

Contribution

It introduces a method to compute QNM frequencies for charged dilaton black holes and shows their quantum spectra are universal and independent of the dilaton parameter.

Findings

Quantum spectra are equally spaced.

Spectra do not depend on the dilaton parameter 'a'.

The dimensionless constant is twice Bekenstein's value.

Abstract

In this study, we employ the scalar perturbations of the charged dilaton black hole (CDBH) found by Chan, Horne and Mann (CHM), and described with an action which emerges in the low-energy limit of the string theory. A CDBH is neither asymptotically flat (AF) nor non-asymptotically flat (NAF) spacetime. Depending on the value of its dilaton parameter "a", it has both Schwarzschild and linear dilaton black hole (LDBH) limits. We compute the complex frequencies of the quasinormal modes (QNMs) of the CDBH by considering small perturbations around its horizon. By using the highly damped QNMs in the process prescribed by Maggiore, we obtain the quantum entropy and area spectra of these BHs. Although the QNM frequencies are tuned by "a", we show that the quantum spectra do not depend on "a", and they are equally spaced. On the other hand, the obtained value of undetermined dimensionless constant {\epsilon} is the double of Bekenstein's result. The possible reason of this discrepancy is also discussed.