Gravitational wave memory and its effects on particles and fields

Gravitational wave memory is said to arise when a gravitational wave burst produces changes in a physical system that persist even after that wave has passed. This paper analyzes gravitational wave bursts in plane wave spacetimes, deriving memory effects for timelike and null geodesics, massless scalar fields, and massless spinning particles whose motion is described by the spin Hall equations. We find that all such effects are characterized by four "memory tensors," three of which are independent. We also show that memory effects for null geodesics can have strong longitudinal components, even in vacuum general relativity. When considering massless particles with spin, we solve the spin Hall equations analytically by showing that there exists a conservation law associated with each conformal Killing vector. For the scattering of fields by gravitational waves, we show that given any solution to the massless scalar field equation in flat spacetime, a weak-field solution in a plane wave spacetime can be generated just by applying an appropriate differential operator -- an operator that is constructed from the aforementioned memory tensors. Memory effects for scalar fields are illustrated for both incoming plane waves and higher-order Gaussian beams. We also present a numerical comparison between the spin Hall equations and the full evolution of localized wave packets with angular momentum. Although we work in plane wave spacetimes, which are physically idealized, similar results are also expected to apply for sufficiently small systems affected by distantly generated gravitational waves. Using the Penrose limit, our results may also apply to ultrarelativistic systems at arbitrary locations in arbitrary (even nonradiating) spacetimes.