Brickwall, Normal Modes and Emerging Thermality

Abstract: In this article, we demonstrate how black hole quasi-normal modes can emerge from a Dirichlet brickwall model normal modes. We consider a probe scalar field in a BTZ geometry with a Dirichlet brickwall and demonstrate that as the wall approaches the event horizon, the corresponding poles in the retarded correlator become dense and yield an effective branch-cut. The associated discontinuity of the correlator carries the information of the black hole quasi-normal modes. We further demonstrate that a non-vanishing angular momentum non-perturbatively enhances the pole-condensing. We hypothesize that it is also related to quantum chaotic features of the corresponding spectral form factor, which has been observed earlier. Finally, we discuss the underlying algebraic justification of this approximate thermalization in terms of the trace of the algebra.