"Swimming" versus "swinging" in spacetime

TL;DR

This paper distinguishes between relativistic 'spacetime swimming' and Newtonian 'space swinging', showing that at high speeds, the relativistic effect dominates, and extends Wisdom's predictions to strong gravitational fields.

Contribution

It clarifies the difference between relativistic and Newtonian cyclic shape deformation effects on bodies in gravitational fields and generalizes Wisdom's effect to strong gravity regions.

Findings

Relativistic 'spacetime swimming' dominates over 'space swinging' at high cycle speeds.

The relativistic effect includes higher order terms beyond Wisdom's original prediction.

The results are extended to bodies in large red-shift regions, applicable to strong gravitational fields.

Abstract

Wisdom has recently unveiled a new relativistic effect, called ``spacetime swimming'', where quasi-rigid free bodies in curved spacetimes can "speed up", "slow down" or "deviate" their falls by performing "local" cyclic shape deformations. We show here that for fast enough cycles this effect dominates over a non-relativistic related one, named here ``space swinging'', where the fall is altered through "nonlocal" cyclic deformations in Newtonian gravitational fields. We expect, therefore, to clarify the distinction between both effects leaving no room to controversy. Moreover, the leading contribution to the swimming effect predicted by Wisdom is enriched with a higher order term and the whole result is generalized to be applicable in cases where the tripod is in large red-shift regions.