Where a Black Hole's Ringing Begins express
When two black holes merge, the newborn object rings like a bell. This ring, gravitational waves of a special kind, astronomers call quasinormal modes (particular damped oscillations). They decay quickly but still reveal the black hole's mass and spin. The question is where in space this ringing begins.
The authors proposed that the mode excitation radius is the point where the character of the wave solution changes. Around a black hole, space is so strongly curved that waves behave differently at different distances. Closer to the hole, they decay in one direction; farther away, in another. At the boundary, a standing wave is born — the ringing itself. For a non-spinning black hole, this radius turned out to be 2.557 times the black hole's mass, not 3 times as for the photon ring.
The team tested the idea numerically: they decomposed the signal into a sum of damped modes and looked at the radius from which this series converges. For moderately spinning holes, the numerical radius matched the analytical one. For a maximally spinning hole, the excitation radius crept almost to the horizon — the boundary from which nothing returns. There, modes with zero damping play the leading role and set the tone.
This means that each mode, each timbre, has its own birth region. Higher overtones 'sound' closer to the hole. Now, when listening to gravitational waves, we understand more precisely where the sound comes from.
The excitation radius of a black hole does not depend on the angle at which the wave falls in, if the overtone is very high: it is always in the same place.
In the movie 'Interstellar', the heroes see a photon ring around the black hole Gargantua — the very one that, as is now clear, is not directly related to its ringing.