Spinning test particles in a weak gravitational wave and the memory effect

Abstract

In this work, we investigate the worldline deviation of spinning test particles in a weak gravitational wave (GW) spacetime. Within the pole-dipole approximation and the Tulczyjew spin supplementary condition, we consider the modified deviation equation, which contains the standard geodesic deviation term and an additional contribution generated by the Mathisson-Papapetrou-Dixon (MPD) force. We demonstrate how the deviation equation can be solved under viable approximations to yield a new expression for the change in the deviation vector in terms of the perturbation $h_{ij}$, its time derivative, the spin vector components and the longitudinal and transverse components of the deviation. The spin-curvature coupling is shown to play a crucial role in controlling the change in deviation. We then use this result to investigate the changes in the form and expressions of the net GW signal as well as our understanding of GW memory, in the presence of spin. We conclude with our attempts on the measurability of this spin-induced effect \emph{vis-a-vis} present GW observations.