Gravity's Effect on Space: Length Contraction & Light Speed

[Akshar Tandon]

This question is inspired by the movie Interstellar but asks a basic question about relativity. Everyone talks about gravitational time dilation but I am wondering if gravity has an effect on space as well, after all it bends space time. I have not found a lot of information on length contraction in the context of gravity (velocity, yes, but not gravity). If we were to look at a clock on a planet with a very strong gravity, we would see time move extremely slow but would we also see the clock stretched/contracted? Also, would light "appear" to travel faster/slower on this planet when externally observed?

 

[A.T.]

I am wondering if gravity has an effect on space as well,

Yes, it does.
http://en.wikipedia.org/wiki/Schwarzschild_metric#Flamm.27s_paraboloid
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.mathpages.com/rr/s8-09/8-09.htm

Also, would light "appear" to travel faster/slower on this planet when externally observed?

Slower:
http://en.wikipedia.org/wiki/Shapiro_delay

I'm not sure though, if the Shapiro delay refers only the effect of gravitational dilation (as wiki says), or to the combined effect including spatial geometry.

 

[PeterDonis]

I'm not sure though, if the Shapiro delay refers only the effect of gravitational dilation (as wiki says), or to the combined effect including spatial geometry.

The formula given on the Wiki page includes both. The factor of $\left( 1 + \gamma \right)$ is the key (where $\gamma$ is one of the PPN parameters); it's the same factor that appears in the formula for light bending by a massive body like the Sun, which takes into account both time and space curvature.