Rescuing the concept of swimming in curved spacetime

TL;DR

This paper critically examines the concept of swimming in curved spacetime, clarifying the conditions under which such motion is possible and correcting previous misconceptions with a covariant formalism.

Contribution

It demonstrates that previous analyses were inappropriate and provides a covariant framework showing swimming in curved spacetime is possible under certain conditions.

Findings

Previous analysis was invalid, leading to incorrect conclusions.

Swimming in curved spacetime can occur and is quantifiable.

Magnitude of swimming can be comparable to earlier predictions, but is generally suppressed.

Abstract

It has been argued that an extended, quasi-rigid body evolving freely in curved spacetime can deviate from its natural trajectory by simply performing cyclic deformations. More interestingly, in the limit of rapid cycles, the amount of deviation, per cycle, would depend on the sequence of deformations but not on how fast they are performed -- like the motion of a swimmer at low Reynolds number. Here, however, we show that the original analysis which supported this idea is inappropriate to investigate the motion of extended bodies in the context of general relativity, rendering its quantitative results invalid and casting doubts on the reality of this swimming effect. We illustrate this by showing that the original analysis leads to a non-zero deviation even in a scenario where no swimming can possibly occur. Notwithstanding, by applying a fully covariant, local formalism, we show that swimming in curved spacetime is indeed possible and that, in general, its magnitude can be of the same order as (fortuitously) anticipated -- although it is highly suppressed in the particular scenario where it was originally investigated.