Gravitational waves leave a permanent displacement in spacetime, remembering past events.Gravitational memory is a subtle but profound effect of general relativity: when gravitational waves pass through spacetime, they not only cause temporary oscillations but also leave a permanent, residual displacement in the relative positions of test masses. This means that after the wave has passed, the spacetime does not return exactly to its original state—it 'remembers' the event. This effect is sometimes called the 'memory effect' or the 'Christodoulou memory'.
The concept was first discussed by Ya. B. Zel'dovich and A. G. Polnarev in 1974, who considered the effect for passing particles. The nonlinear contribution was later rigorously derived by Demetrios Christodoulou in 1991, and the effect is now a standard prediction of general relativity.
The memory effect arises from the nonlinear nature of gravity. The gravitational waves themselves carry energy, and this energy contributes to the spacetime curvature. When a burst of gravitational waves passes, the energy distribution changes, leading to a permanent change in the metric. For a detector, this manifests as a step-like change in the separation of two test masses, which persists after the oscillatory part of the wave has faded. There are also linear contributions from the motion of the source, but the nonlinear part is particularly interesting because it is a direct consequence of the self-interaction of gravity.
Detecting gravitational memory would provide a unique test of general relativity's nonlinear structure. It is a target for future gravitational wave observatories, as the effect is small and requires long-duration observations or very sensitive detectors.
The memory effect is so subtle that for a typical binary black hole merger, the permanent displacement it leaves on a detector like LIGO is only about a billionth of a proton's diameter.





