A gravitational wave is a propagating disturbance of spacetime curvature produced by changing mass-energy multipole moments.
Forthe only potentially nonzero Ricci component isThe vacuum equation is therefore the transverse Laplace equation.
A gravitational-wave pulse has curvature supported in a bounded interval of retarded time. Spacetime can be flat both before and after the pulse even though freely falling bodies retain a displacement or relative velocity produced while the pulse passed.
The gravitational-wave memory effect is a lasting change in the relative configuration of freely falling test bodies after a transient gravitational wave has passed.
Displacement memory is a persistent change in the separation of freely falling bodies after a gravitational-wave pulse.
Velocity memory is a persistent change in the relative velocity of freely falling bodies after a gravitational-wave pulse.
