# Gravitational Length Contraction

1. Apr 5, 2013

### nigelscott

I understand the concepts of time dilation and length contraction in SR. I also understand the concept of time dilation in a gravitational field. But what about length contraction in a gravitational field? Is there such a thing and can it be derived from the Schwarzchild metric?

2. Apr 5, 2013

### Agerhell

I believe that in the Schwarzschild solution expressed in Schwarzschild coordinates the speed of light is anisotropic and that in order to explain this a "gravitational length contraction" in the radial direction is sometimes thought of.

3. Apr 5, 2013

### pervect

Staff Emeritus
A lot of lay people seem to think that gravitational length contraction should exist for reasons that are unclear, but I don't think I've ever seen a textbook or paper discussing the concept specifically. (It's possible I could have missed a paper on the topic, of course.)

Going from analogy with time dilation, though, I'd guess one could define it as the ratio between proper distance and changes in coordinates.

The value of this ratio will be dependent on the coordinates used of course, just as in the case of time dilation. So I dont see any coordinate-independent significance to the term.

4. Apr 5, 2013