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Foliating spacetime

  1. Apr 10, 2009 #1

    naima

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    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: Apr 24, 2017
  2. jcsd
  3. Apr 10, 2009 #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.
     
  4. Apr 10, 2009 #3

    naima

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    Great

    This is exactly what I was looking for.
     
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