Secondary waves in a black hole's ringdown, born from the nonlinearity of spacetime.Overtones are additional, higher-frequency oscillations that appear in the gravitational-wave signal emitted by a black hole immediately after it forms from a merger. This 'ringdown' phase is characterized by a dominant fundamental mode, but overtones arise from the nonlinearity of spacetime near the black hole, adding complexity to the signal. Detecting overtones allows scientists to test general relativity in the strong-field regime and to measure the properties of the newly formed black hole with greater precision.
The theoretical framework for black-hole ringdown and overtones was developed in the 1970s by Saul Teukolsky and others, who derived the equations governing perturbations of black holes. The first clear detection of an overtone in a gravitational-wave signal was reported in 2019, from the merger event GW150914.
When two black holes merge, the resulting black hole is initially distorted, and it settles into a spherical shape by emitting gravitational waves. This emission is a superposition of quasi-normal modes—oscillations with specific frequencies and damping times. The fundamental mode is the loudest, but overtones have higher frequencies and decay faster. The nonlinearity of Einstein's equations means that these modes are not independent; they interact, producing subtle features in the signal that can be extracted with careful analysis.
Overtones are used to test the 'no-hair theorem' of black holes, which states that a black hole is fully described by its mass, spin, and charge. Measuring multiple modes provides a stringent check of this prediction of general relativity.
The overtone frequencies of a black hole are like the harmonics of a bell, but they decay so quickly that they last only a few milliseconds, making them one of the most fleeting signals in astrophysics.















