Quasi-normal modes and microscopic description of 2D black holes

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 $$ \hat{\omega} $$ ω ̂ . We further model the black hole as a statistical ensemble of N decoupled quantum oscillators of frequency $$ \hat{\omega} $$ ω ̂ . 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.

Effective models of non-singular quantum black holes

“…Our findings only partially confirm Hod's conjecture on zero-damped QNMs for standard extremal black holes [69][70][71][72][73][74][75]. On the other hand, this result is perfectly consistent with the AdS 2 × S 2 behavior of the near-horizon, near-extremal metric and with what is known about the QNMs spectrum of 2D AdS gravity models [64][65][66][67][68].…”

“…Conversely, black holes with ∼ R S are characterized by macroscopic deviations from the Schwarzschild behavior, whose signatures are potentially detectable by the next generation of GW detectors. In particular, by analytically computing the QNMs spectrum in the eikonal approximation, we find that, in the near-extremal limit, the imaginary part of the quasi-normal frequencies scale with the black-hole temperature as c 1 / + c 2 T 2 H (with c 1,2 constants), while in the near-extremal and near-horizon regimes, it goes to zero, in agreement with several results in the literature [64][65][66][67][68][69][70][71][72][73][74][75].…”

“…One family, corresponding to the simple near-extremal limit has indeed a non vanishing imaginary part in the extremal limit, while the other branch shows that the damped part of the spectrum goes to zero in the near-extremal, near-horizon limit. Moreover, the temperature scaling (50) fully confirms previous derivation of the quasinormal spectrum for two dimensional AdS 2 black holes [64][65][66][67][68]. In fact, the latter allows for an explicit analytical treatment through different methods, which all point towards the same result: a linear scaling of the imaginary part ω I with the temperature of the hole.…”

Gravitational traces of bumblebee gravity in metric–affine formalism

“…The investigation of quasinormal modes of black holes has extensively utilized the weak field approximation in the literature, both in general relativity (GR) [42,[44][45][46][47][48][49][50][51][52][53][54][55][56][57] and in alternative gravity theories such as Ricci-based theories [58][59][60], Lorentz violation [61,62], and related fields [32,[63][64][65][66].…”

Analysis of a regular black hole in Verlinde’s gravity

“…The study of quasinormal modes of black holes has been extensively conducted in the literature, employing the weak field approximation. This approach has been applied not only in the framework of GR [30,54,[56][57][58][59][60][61][62][63][64][65][66][67][68], but also in alternative gravity theories including Ricci-based theories [69][70][71], Lorentz violation [72,73], and other related fields [74][75][76][77][78].…”