Abstrakt
The motion of a system of test point masses acting on one another in curved space-time is, in general, different from the motion of a single test point mass, i.e. different from a geodesic. A simple example of such a body is a glider consisting of two point masses, whose coordinate distance changes as a predefined function of time.
This model predicts the presence of the swimming effect in the case of a radial fall into a Schwarzschild black hole. However, the unphysical nature of the model is inconsistent with Dixon's theory of extended bodies in general relativity as we confirm by using the model in maximally symmetric space-times.
We propose a more physically plausible discrete model of a dumbbell-like body involving the exchange of momentum via interaction particles with negative rest energy. The behaviour of this model in maximally symmetric space-times agrees with Dixon's theory.
Furthermore, we show that the apparent swimming effect from the glider model disappears in the discrete model, complying with the Newtonian case.