# Movement in curved spacetime via deforming one's body

Apologies if this is the wrong topic, but I think it's relevant under GR since it involves curved space time and I can't see it applying to Newtonian systems.

I found an article about swimming in space by deforming one's body. This should not be possible according to my understanding of classical physics, but in curved spacetime it apparently can work.

Now the problem is, I understand how it can be done from the links provided, but I lack the formal mathematical training to make any notion of how fast one could move, or how big one would need to be in order to gain a useful velocity.

The links to the paper, and to a "pop sci" website that explains it with animations

http://dspace.mit.edu/handle/1721.1/6706

http://www.science20.com/hammock_physicist/swimming_through_empty_space

How would I go about calculating this?

Basic calculus (integration by parts etc) and matrix transforms for 3d computer graphics is the limit of my mathematical knowledge.

## Answers and Replies

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Now the problem is, I understand how it can be done from the links provided, but I lack the formal mathematical training to make any notion of how fast one could move, or how big one would need to be in order to gain a useful velocity.
My understanding of the articles is that you can't gain any momentum by 'swimming'. It would violate conservation of momentun if you could. Every stroke (sequence of actions) changes the position of the swimmer without changing momentum. So the 'velocity' of the swimmer is just the distance moved per stroke times the rate of strokes.

There is a another thread in this forum discussing this

https://www.physicsforums.com/showthread.php?t=326206

That's a good point, there's no accumulated momentum. So likely the distance you move will be exceedingly small and therefore probably useless. Unless you're near a black hole where space is highly curved ... but then you're probably finished anyway and therefore probably equally useless :-)