This paper shows that the damped vibrations of a black hole, known as quasinormal modes (QNMs), can be used to learn about the black hole’s interior. The authors demonstrate a way to read a key number that describes how the metric blows up at the singularity — the ‘‘scaling exponent’’ — from the spectrum of highly damped (large‑overtone) QNMs of a simple test field. They then apply the method to an exact family of quantum-corrected black holes in (2+1)-dimensional anti‑de Sitter (AdS) space and find a clear change, deep inside the hole, where quantum effects take over the classical behavior.

What the researchers did is largely analytical. They probe the black hole with a minimally coupled massless scalar field. After separating variables, the radial part of the field equation is turned into a one‑dimensional Schrödinger‑like problem. The authors analytically continue the radial coordinate into the complex plane and follow special directions called Stokes lines. By matching solutions near three regions—the asymptotic AdS boundary, the horizon, and the region near the curvature singularity—they obtain an asymptotic quantization condition for the QNM frequencies. The offset in that condition is directly tied to the scaling exponent of the metric near the singularity, so the QNM spectrum encodes information about the interior.

This matters because it gives an indirect and safe way to probe the near‑singularity geometry without entering the black hole. Near a generic spacelike singularity the geometry follows a power‑law pattern described by Kasner exponents, which tell you how different directions in space shrink or grow as you approach the singularity. The authors apply their method to the exact ‘‘quantum’’ BTZ (qBTZ) black hole and report explicit evidence of a transition from a classical Kasner regime to a quantum‑dominated regime, what they call a Kasner eon transition. In plain terms, their results suggest QNMs could signal where quantum gravity changes the interior structure.