Analytical Study of Spin–Gravity Coupling in Plane Gravitational Wave Spacetimes
Analytical Study of Spin–Gravity Coupling in Plane Gravitational Wave Spacetimes
In this note, using existing methods, we investigate spin-gravity coupling in a plane gravitational wave spacetime via the Mathisson–Papapetrou–Dixon (MPD) equations. Working in Rosen coordinates for their geometric simplicity, we examine the MPD equations to first order in spin. Our analysis shows how projecting the spin vector onto a parallel-transported orthonormal tetrad leads to conserved quantities, and how spin-curvature coupling gives rise to deviations from geodesic motion. The approach we follow does not rely on a specific wave profile or initial conditions, allowing for a general treatment of plane gravitational waves with arbitrary polarization.
Analytical Study of Spin–Gravity Coupling in Plane Gravitational Wave Spacetimes