Brickwall model for hyperbolic black holes and chaos

Abstract: We study the quantum chaotic behavior of black holes within the brickwall model, focusing on probe scalar fields in ($d+1$)-dimensional hyperbolic AdS black holes. The brickwall model has captured the normal modes of BTZ black holes ($d=2$) with Gaussian-distributed boundary conditions on the stretched horizon and their connection to quantum chaos signatures of random matrix theory. Here, we extend this framework to higher-dimensional AdS black holes ($d>2$), exploring how black hole normal modes encode chaotic dynamics across dimensions and examining the universality of this approach. We show that quantum chaos is prominent in lower dimensions and persists in higher dimensions. Specifically, deviations from the logarithmic spectrum in $d=2$ evolves into a power-law spectrum at higher $d$, highlighting the sensitivity of black hole normal modes to dimensionality, while retaining signatures of quantum chaos despite the spectral deformation. Our results are supported by conventional diagnostics, including level spacing distributions and spectral form factors, as well as modern tools like Krylov complexity. Finally, we discuss the limitations of the brickwall model in capturing chaotic behavior in the parametrically large dimension limit, where the spectrum becomes constant leading to degeneracy and a non-chaotic regime, while emphasizing its effectiveness as a tool for studying quantum aspects of black holes in moderate higher dimensions.