Drop a stone into a pond — the ripples spread and fade away. A black hole, after colliding with another hole or a star, also 'rings', but its oscillations are not simple. Near the hole, 'overtones' sound — secondary waves born from the nonlinearity of spacetime itself. Far from the hole, at infinity, an indelible trace remains — the 'memory' of the passing wave. These two phenomena seemed distinct, but now they have been linked into a single picture.
The bridge consists of coefficients that depend on the mass and spin of the remnant black hole. They show how the energy of nonlinear oscillations is transferred into the 'memory'. If future detectors, such as the space-based telescope LISA, catch gravitational waves from black hole mergers, they will be able to measure these coefficients. Then Einstein's general relativity will get another test in the nonlinear regime.
Thus, the ring and the memory of a black hole turn out to be two sides of the same coin. The ripples on the pond die down, but the bottom remembers that a wave crossed the water.
The memory effect was predicted by Demetrios Christodoulou in 1991: a gravitational wave permanently changes the distance between two points in space.
In the movie 'Interstellar', the characters use gravitational anomalies near a black hole to send a message into the past, the nonlinear effects of spacetime are artistically portrayed there.