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Brick wall in an AdS-Schwarzschild black hole: Normal modes and emerging thermality

Suman Das1,*, Somnath Porey2,†, and Baishali Roy2,‡

  • *Contact author: suman.das@saha.ac.in
  • †Contact author: somnathhimu00@gm.rkmvu.ac.in
  • ‡Contact author: baishali.roy025@gm.rkmvu.ac.in
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Phys. Rev. D 112, 106013 – Published 24 November, 2025

DOI: https://doi.org/10.1103/dqnb-kg1z

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 nontrivial 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. This feature appears to vanish when the horizon size becomes much larger compared to the anti–de Sitter length. 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 anti–de Sitter/conformal field theory correspondence.

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Phys. Rev. D 112, 106013– Published 24 November, 2025
  • Received 19 April 2025
  • Accepted 10 October 2025
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