A black hole can be compared to a bell: after being struck, it vibrates, emitting a decaying 'ring.' This ring is the gravitational waves that detectors on Earth pick up. Typically, astrophysicists listen to the overtones generated by the light ring — the region near the horizon where photons circle before falling in or escaping. But the authors of the new study made the hole grow slowly by feeding it matter, and they heard something new.
In the growing black hole, alongside the familiar overtones, purely imaginary frequencies emerged. A pendulum that swings ever slower but suddenly just falls without oscillating: that's an analogy for such a signal. An analytical calculation using the sophisticated Heun functions and numerical simulations on hyperboloidal slices matched perfectly. These imaginary modes govern the very end of the signal: when the ordinary ring has already faded, they create an exponentially decaying tail.
Time-domain simulations confirmed that the purely imaginary tones are not a mathematical curiosity but a real physical effect. When the hole stops growing, the spectrum returns to the classic power-law tail. This discovery provides a new tool for analyzing data from gravitational wave detectors and testing curved spacetime near the horizon.
The power-law tail in an ordinary black hole is like an echo in a large hall: the sound fades slowly and smoothly. The exponential tail is like a finger snap in a small room: it appears abruptly and is gone in an instant.
In Stanislaw Lem's novel 'Solaris,' the ocean generated mysterious structures as if responding to human thoughts. Similarly, a black hole 'responds' to mass growth with a new type of signal, as if finding its voice.