Foliating spacetime

  • Thread starter naima
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  • #1
naima
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Main Question or Discussion Point

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.
 
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  • #2
atyy
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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
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Great

This is exactly what I was looking for.
 

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