Quasinormal modes of coupled metric-dilaton perturbations in two-dimensional stringy black holes

TL;DR

This paper analyzes the quasinormal modes of coupled metric-dilaton perturbations in two-dimensional stringy black holes, revealing their stability and oscillatory behavior through numerical spectrum analysis.

Contribution

It provides the first detailed numerical study of intrinsic coupled perturbations in 2D stringy black holes, highlighting their stability and oscillation characteristics.

Findings

All modes satisfy Im(ω)<0, confirming stability.

Intrinsic perturbations exhibit nonvanishing real parts, indicating oscillatory modes.

Increasing the central-charge parameter reduces damping and prolongs relaxation.

Abstract

We investigate the quasinormal modes (QNMs) associated with intrinsic metric-dilaton coupled perturbations of the Mandal-Sengupta-Wadia (MSW) black hole in two-dimensional string theory. Through suitable field redefinitions, the gravity-dilaton system is expressed in terms of the conformal factor and a redefined dilaton field, allowing the linear perturbation equations to be reduced to coupled Schrodinger-type eigenvalue equations in the tortoise coordinate. By imposing the standard QNMs' boundary conditions of purely ingoing waves at the horizon and purely outgoing waves at spatial infinity, we numerically determine the complex frequency spectrum. All modes satisfy Im$(\omega)<0$, confirming the linear stability of the MSW black hole under intrinsic coupled perturbations. Unlike external scalar-field perturbations, which yield purely imaginary frequencies, the intrinsic perturbations generically exhibit nonvanishing real parts, corresponding to oscillatory modes of the gravity-dilaton sector. The real part of the frequency displays a nonmonotonic dependence on the overtone number, while increasing the central-charge parameter $\sqrt{k}$ systematically decreases the damping rate and prolongs the relaxation time. These results indicate that intrinsic perturbations probe internal dynamical degrees of freedom and reveal characteristic features of the relaxation dynamics of two-dimensional stringy black holes.