The Galilean equivalence principle (or weak equivalence principle) is the statement of the universality of free-fall under gravity. For example, according to Wikipedia, it can be stated as follows My question regards the limitation of the principle to point masses. Does universality of free-fall not hold for extended objects? It seems to me that in Newtonian gravity if one focuses on the center of mass of a body universality of free-fall is satisfied. What about GR? If the particle is point-like, it is well-known that universality of free-fall is embodied in the fact that the particle trajectories are the geodesics of the spacetime manifold. Do extended objects move geodetically? I assume the object is extended but still has a small mass, so that one can neglect the gravitational influence of the object.