A black hole rings like a bell after being struck. This ring is the gravitational waves that detectors pick up. But what changes if the space around the hole is curved not only by its mass but also by an additional quantum correction? The authors added the Gauss–Bonnet term to Einstein's equations, a kind of 'ripple' on the fabric of spacetime, and traced how the sound depends on it.
They calculated the oscillation spectrum (quasinormal modes) for black holes in worlds with dimensions ranging from five to twenty-six. A precise numerical method allowed them to peer where the usual approximate formulas no longer work. It turned out that the Gauss–Bonnet correction strongly changes the 'voice' of the hole: purely damped tones appear, without oscillations, and the frequency of high overtones can behave unexpectedly: first rising, then falling.
In the scalar and vector sectors, an exact isospectrality was found: two different modes oscillate with the same frequencies as long as the Gauss–Bonnet correction is turned off. The authors proved this analytically by factoring the Hamiltonians, as in high-school algebra. For tensor modes, no such coincidence exists, and it is precisely there that the instability hides. Converting to physical frequencies showed that enhanced oscillations in higher-dimensional models could fall within the sensitivity range of the future space-based detector DECIGO.
The term 'quasinormal modes' was introduced in the 1970s by Indian physicist Vishveshwara, who compared the damped oscillations of a black hole to the ringing of a bell that gradually fades.
In Carl Sagan's novel 'Contact', the alien signal contains a corrected version of the number π, hinting at a hidden structure of the universe — much like the Gauss–Bonnet correction reveals itself in the 'sound' of black holes in higher dimensions.