# Foliating spacetime

1. Apr 10, 2009

### naima

Hi all,

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.

Last edited by a moderator: Apr 24, 2017
2. Apr 10, 2009

### 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.

3. Apr 10, 2009

### naima

Great

This is exactly what I was looking for.