CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses

TL;DR

This paper employs conformal field theory and localization techniques to derive exact formulas for wave propagation in black hole and exotic compact object backgrounds, analyzing phenomena like QNMs, superradiance, echoes, and tidal responses.

Contribution

It introduces a CFT-based framework to compute wave behavior and proposes a new definition of dynamical Love numbers for gravity.

Findings

Exact connection matrices for wave functions near singularities

Application to QNMs, echoes, and tidal responses of BHs and ECOs

Proposal of a new dynamical Love number concept

Abstract

Using conformal field theory and localization tecniques we study the propagation of waves in gravity backgrounds described by Schr\"odinger like equations with Fuchsian singularities. Exact formulae for the connection matrices relating the asymptotic behaviour of the wave functions near the singularities are obtained in terms of braiding and fusion rules of the CFT. The results are applied to the study of quasi normal modes, absorption cross sections, amplification factors, echoes and tidal responses of black holes (BH) and exotic compact objects (ECO) in four and five dimensions. In particular, we propose a definition of dynamical Love numbers in gravity.