Foliating spacetime

  • Thread starter naima
  • Start date
  • #1
naima
Gold Member
938
54
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, [tex] \Sigma_t [/tex], labeled by a global time function, t.
for each point of [tex] \Sigma^t [/tex] there is a vector [tex]n_\mu[/tex] 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:

Answers and Replies

  • #2
atyy
Science Advisor
14,346
2,588
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
naima
Gold Member
938
54
Great

This is exactly what I was looking for.
 

Related Threads on Foliating spacetime

  • Last Post
Replies
6
Views
3K
Replies
2
Views
856
  • Last Post
4
Replies
92
Views
13K
Replies
6
Views
2K
Replies
4
Views
259
  • Last Post
Replies
1
Views
632
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
20
Views
7K
Replies
3
Views
779
Replies
11
Views
1K
Top