A black hole is not a dead object. After a disturbance, such as merging with another hole, it rings like a bell. This ring is not just a sound but a complex set of damped oscillations called quasinormal modes. Their frequency and damping rate depend on the hole itself: its mass, charge, and spin.
In the new work, scientists considered charged black holes in a special type of space — anti-de Sitter (which resembles a concave saddle). It turns out that as temperature changes, such a hole can restructure in a jump: first being large, then shrinking to small, and then expanding again to an intermediate size. This is similar to a reentrant phase transition known from some liquids and alloys. But here — on the scale of the event horizon.
The authors solved the Klein-Gordon equation for a massless scalar field using the shooting method and computed quasinormal mode frequencies for each phase. The frequencies clearly differed: the small hole rang on one note, the large on another, and the intermediate on a third. Thus, physicists obtained a "voiceprint" for each thermodynamic phase. Now, by listening to the ring of distant black holes, we can tell whether they are undergoing an internal restructuring, just as the sound of pouring water distinguishes hot from cold.
Reentrant phase transitions, like the one found in black holes, occur in everyday life: for example, a mixture of nicotine and water, when heated, first mixes, then separates, and then mixes again.
In Stanislaw Lem's novel "Solaris," the planet's ocean spawned complex structures reminiscent of quasinormal modes — damped oscillations that retain memory of past states.