Massless spinning test particles in a gravitational field

The classical equations of motion of a massless spinning test particle are derived as a limiting case of Mathisson-Papapetrou equations. It is shown that when a particular supplementary condition is assumed the particle follows a null geodesic and the spin is either parallel or antiparallel to the direction of motion. Moreover, the helicity is conserved in an orientable spacetime. The equations of the propagation of the momentum vector and the spin tensor along the trajectory are given and further implications of the solution are discussed.