Brick Wall in AdS-Schwarzschild Black Hole: Normal Modes and Emerging Thermality

TL;DR

This paper studies the normal modes of a scalar field near a five-dimensional AdS-Schwarzschild black hole's horizon, revealing how boundary conditions influence spectral properties and lead to emergent thermality, with implications for black hole microstates and chaos.

Contribution

It extends analysis of black hole normal modes and spectral features to higher dimensions, demonstrating the impact of the brick wall boundary condition on emergent thermal behavior.

Findings

Spectral spectrum depends linearly on principal quantum number.

Spectral form factor exhibits dip-ramp-plateau structure.

Poles of Green's function condense as brick wall approaches horizon.

Abstract

This paper investigates the normal modes of a probe scalar field in a five-dimensional AdS-Schwarzschild black hole with the brick wall boundary condition near the horizon. We employ various techniques to compute the spectrum and analyze its properties. Our results reveal a linear dependence of the spectrum on the principal quantum number while demonstrating a non-trivial dependence on the angular momentum quantum number. We compute the Spectral Form Factor (SFF) and find a dip-ramp-plateau structure, with the slope of the ramp approaching unity as the brick wall nears the horizon. We also observe that as the brick wall approaches the horizon, the poles of the retarded Green's function condense on the real line, leading to an emergent thermal behavior in the boundary theory. This work extends previous studies on lower-dimensional black holes to higher dimensions, providing insights into the connection between black hole microstate models and boundary chaos. Our findings contribute to the ongoing discussions on the information paradox and the nature of black hole interiors in the context of AdS/CFT correspondence.