Foliating Spacetime: Understanding the Curves and Metrics

[naima]

Hi all,

I began to read this paper :http://www.physics.adelaide.edu.au/mathphysics/abstracts/ADP-95-11-M28.html"
On page 9 the author foliates spacetime into spatial hypersurfaces, $$\Sigma_t$$, labeled by a global time function, t.
for each point of $$\Sigma^t$$ there is a vector $$n_\mu$$ orthogonal to it
These vectors generate a flow on spacetime.
Physically what are these curves? are they geodesics?
Have you links using his notations for the intrinsic metric?

thanks.

 

[atyy]

For the choice N=1, they are geodesics. See the discussion just before Eq 4.77 of Gourgoulhon's http://arxiv.org/abs/gr-qc/0703035. His discussion also says it's not always possible to make this choice over the entire spacetime.

 

[naima]

Great

This is exactly what I was looking for.