Exact solutions for the motion of spinning massive particles in conformally flat spacetimes

The motion of massive spinning test particles (tops) on gravitational backgrounds is studied based on a Lagrangian formulation developed some forty years ago. In particular, the (non-geodesical) equations of motions on some conformally flat spacetimes are solved exactly. Since tops follow non-geodesical paths, velocity and momentum vectors are, in general, non- paralell. Some peculiar features such as superluminal motion are exhibited and discussed in some detail. (paper)