Abstract: In General Relativity the trajectories of real extended test bodies depend on its properties, due to the coupling of the field to the bodys multipole moments (only idealized, monopole point particles move along geodesics!). One of the challenges in the description of extended bodies is the choice of a worldline that adequately represents its motion. The center of mass is a natural choice; however, unlike the situation in Newtonian mechanics, in relativity such point is observer dependent. Its fixing is done through the so-called spin supplementary condition --- an old problem in this context, and still not well understood.
In this talk I shall discuss the problem of defining the center of mass in General Relativity and the different spin conditions in the literature. Their physical significance, the reason for the non-parallelism between the velocity and the momentum, and the concept of hidden momentum, will be dissected. It will be argued that the different solutions allowed by the different spin conditions are equally valid descriptions for the motion of a given test body, and their equivalence proved to dipole order in a curved spacetime. Finally I will compare the different conditions in simple examples in flat and curved spacetimes, and summarize the pros and cons of each of them.
Place: Physics Dept. Meeting Room, 2th floor, IST