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Explanation of word foliation in quantum gravity?

  1. Feb 25, 2010 #1
    explanation of word "foliation" in quantum gravity?

    I please for explanation of word "foliation" in quantum gravity?
     
  2. jcsd
  3. Feb 25, 2010 #2

    bapowell

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    Re: foliation

    A foliation is a prescription for coordinitizing spacetime. It is an aspect of general relativity, and is not specific to quantum gravity. When you 'foliate' a spacetime, you define spacelike hypersurfaces and give a prescription for how these hypersurfaces evolve in time. In short, you 'fill' the spacetime manifold with hypersurfaces such that for every point x in the manifold, there is a hypersurface that contains it. As a simple analogy, allow a book to represent a 3D spacetime. Then, the 2D pages of the book are your hypersurfaces, and the page numbers define how you go from one to the next: the pages and page numbers make up your foliation.
     
  4. Feb 25, 2010 #3

    marcus

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    Re: foliation

    Good explanation!
    Foliage means leaves.
    A folio is a book.
    A portfolio is a kind of flat box to keep pages or drawings, any kind of flat stuff, in.

    A foliation of spacetime is a way of slicing it up. For example into "time-slices" which are sheets consisting of events that some observer considers to be simultaneous. Different observers will slice it differently.
     
  5. Feb 25, 2010 #4

    tom.stoer

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    Re: foliation

    Foliation does only apply to spacetimes with global structure R*M³, where M³ is a spacelike manifold.
     
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