Title: Swimming in curved spacetime: a fully covariant approach
Abstract: It has been argued that a free extended body, performing fast cyclic internal motions, could propel itself through the curved spacetimes of general relativity in a "non-dynamical" manner, i.e., such that the resulting motion would not depend on the rapidity of the internal movements but only on the sequence of geometrical shapes assumed by the body. This phenomenon has been named swimming in curved spacetime due to the resemblance to the motion of swimmers in non-turbulent viscous fluids. Based on Dixon's theory of dynamics in general relativity, we develop a fully covariant theory of swimming. We find that although the original analysis supporting this idea is incorrect, the effect can indeed take place, but only in special circumstances. Our methods go much beyond the swimming phenomenon, providing a general description of the motion of small, articulated bodies in curved spacetimes using a formal map to an analogue problem in special relativity.