Motion of a spinning test particle in Vaidya's radiating metric

The motion of a spinning test particle in Vaidya's gravitational field is considered in the framework of Papapetrou's equations of motion. Use is made of the supplementary condition Su = 0, where u is the retarded Schwarzschild time coordinate. We derive the equations for the dynamical variables, and consider the conservation laws, that follow from the equations of motion. Particular cases of motion are also discussed and additional first integrals corresponding to these cases are found. Some of the new extra integrals are related to the Casimir operators of the Poincaré group. It is found that under special conditions on the spin tensor components the particle follows a geodesic. Motion of the spinning test particle in the Schwarzschild field is considered as one of the particular cases.