A black hole cooled to nearly absolute zero resembles a musical instrument with only a limited set of possible notes. Strike it, and it will respond not with any sound, but only with a strictly defined set of frequencies. This is the picture painted by a new study by physicists who investigated the so-called 'pole skipping' (a phenomenon where the system's response loses information about the perturbation) near extremal black holes: those whose temperature tends to zero.
The authors developed a method to expand the complex equations near the horizon in powers of temperature, like peeling an onion layer by layer. Each layer turned out to be independent: the point at which the black hole stops 'remembering' the details of the perturbation depends only on the internal quantum number (the mode index of the black hole), not on the layer number. This led to a surprising conclusion: as the temperature approaches zero, all layers merge, and the allowed values become discrete, like a ruler with sparse tick marks.
Verification on a specific model (the Gubser–Rocha dyonic black hole) confirmed the analytical predictions. It turned out that for large layer numbers, the allowed momenta grow linearly, like steps of a staircase descending into the microcosm. This result opens the way to studying holographic quantum systems at low temperatures without cumbersome calculations — one only needs to know the horizon geometry and the masses of the fields.
As the temperature of a black hole approaches absolute zero, its response to perturbations becomes discrete, like notes on a piano keyboard, where you can only press existing keys, but not the sound between them.
In Stanisław Lem's novel 'Solaris', the ocean exhibited selective reactions to human stimuli — somewhat reminiscent of the discrete response of an extremal black hole from this work.