Explanation of word foliation in quantum gravity?

[exponent137]

explanation of word "foliation" in quantum gravity?

I please for explanation of word "foliation" in quantum gravity?

 

[bapowell]

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.

 

[marcus]

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.

 

[tom.stoer]

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