Abstract
We investigate the possibility of using quasi-normal modes (QNMs) to probe the microscopic structure of two-dimensional (2D) anti-de Sitter (AdS2) dilatonic black holes. We first extend previous results on the QNMs spectrum, found for external massless scalar perturbations, to the case of massive scalar perturbations. We find that the quasi-normal frequencies are purely imaginary and scale linearly with the overtone number. Motivated by this and extending previous results regarding Schwarzschild black holes, we propose a microscopic description of the 2D black hole in terms of a coherent state of N massless particles quantized on a circle, with occupation numbers sharply peaked on the characteristic QNMs frequency hat{omega} . We further model the black hole as a statistical ensemble of N decoupled quantum oscillators of frequency hat{omega} . This allows us to recover the Bekenstein-Hawking (BH) entropy S of the hole as the leading contribution to the Gibbs entropy for the set of oscillators, in the high-temperature regime, and to show that S = N. Additionally, we find sub-leading logarithmic corrections to the BH entropy. We further corroborate this microscopic description by outlining a holographic correspondence between QNMs in the AdS2 bulk and the de Alfaro-Fubini-Furlan conformally invariant quantum mechanics. Our results strongly suggest that modelling a black hole as a coherent state of particles and as a statistical ensemble of decoupled harmonic oscillators is always a good approximation in the large black-hole mass, large overtone number limit.
Highlights
√ r0 = P NG, at which the dynamics deviates from the Newtonian behavior [1,2,3]
Motivated by this and extending previous results regarding Schwarzschild black holes, we propose a microscopic description of the 2D black hole in terms of a coherent state of N massless particles quantized on a circle, with occupation numbers sharply peaked on the characteristic quasi-normal modes (QNMs) frequency ω
We investigated the QNMs spectrum for external massless and massive scalar perturbations in the gravitational background of 2D JT black holes
Summary
Quasi-normal modes (QNMs) represent the characteristic oscillations of a black hole reacting to external perturbations. In JT gravity, the presence of a further degree of freedom (DOF), i.e. the dilaton, allows for the existence of global modes, but not for vectorial nor tensorial propagating ones In this theory, QNMs are linked only to external scalar perturbations of the black hole space-time (2.2). We adopt usual boundary conditions for QNMs requiring Dirichlet conditions at infinity, i.e. the radial function has to behave as R(r) ∼ 0 at r → ∞, and we must have purely ingoing modes at the horizon. Notice that the quasi-normal frequencies are purely imaginary and the resulting modes purely damped This fact derives from the asymptotic AdS2 behavior of the JT black hole, which is reflected in the form of the potential and in the related boundary conditions
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have