A stone drops into a pond — ripples spread and fade. Strike a bell, and it hums at its own pitch. A black hole, after being perturbed, also 'rings,' emitting gravitational waves of a decaying tone. This ring is called quasi-normal modes (special oscillations of spacetime), and its frequency depends on what's inside the hole.

Usually, at the center of a black hole lurks a singularity — a point where density and curvature become infinite, and Einstein's equations lose meaning. But in the Bonanno–Reuter model, born from the idea of asymptotically safe gravity (an approach where gravity doesn't grow to infinity at short distances), quantum corrections smooth out the sharp point. At high energies, gravity stops growing, and the infinity disappears — leaving a smooth core, like a tiny universe with constant density.

The authors applied, for the first time, a spectral method to such a hole — an ultra-precise mathematical tool that decomposes oscillations into pure tones, like a tuner listening to a grand piano. Previous calculations, like an old tuner, caught only the fundamental notes. The new approach revealed whole families of overtones and, crucially, purely imaginary, 'overdamped' modes: those that decay without oscillating, like a blanket muffling sound. Previously, they were simply missed.

Such a detailed spectrum is like fingerprints for a black hole. If future gravitational-wave detectors pick up a similar pattern, we'll have the first evidence that inside a hole there's not a cliff but a continuation, and quantum gravity has left its mark there.