What is the Meaning of Foliate in Physics and Spacetime?

[Haorong Wu]

TL;DR Summary

Does "foliate" mean "consist of"?

Hi, there. I encounter the word "foliate" in GR textbooks but I have not seen it in other physics textbooks before. For example, it reads, we argue that a spherically symmetric spacetime can be foliated by two-spheres, from page 197 in spacetime and geometry by Carroll.

By this sentence, I guess maybe "foliate" means "consist of" such that the spherically symmetric spacetime can be peeled into a family of two-spheres. I am not sure if this is correct, and maybe it implies other meanings?

 

[Dale]

It means to partition one manifold into a series of sub-manifolds of lower dimensions. Like an onion is a 3D ball that is foliated into 2D spheres.

 

[martinbn]

Wikipedia has a page on foliations.

 

[Ibix]

Foliate means to turn into leaves. The intended imagery is slicing 4d spacetime into a stack of 3d "leaves". For example if you take Minkowski spacetime and pick a frame then the set of surfaces of constant time in that frame are a foliation of that spacetime.

 

[Haorong Wu]

Thanks, @Dale , @martinbn , @Ibix !

So "foliate" does have a meaning close to "consist of". I get the image now.

 

[Dale]

Well, the root of the word is about leaves, as in “foliage”. So it is not merely “consist of” which could separate the thing into chunks rather than leaves. That is why I used the example of an onion, since the layers of an onion are formed by modified leaves.

 

[Bandersnatch]

foliage

leaves

On a tangential note, I've always thought the etymology comes more immediately from the folia of a book (i.e. sheets of paper) rather than from literal leaves at the root of the word. The imagery being that of a seemingly solid whole being separated into many stacked thin sheets.

 

[Ibix]

On a tangential note, I've always thought the etymology comes more immediately from the folia of a book (i.e. sheets of paper) rather than from literal leaves at the root of the word. The imagery being that of a seemingly solid whole being separated into many stacked thin sheets.

Indeed, but that comes from the same root folium, which means leaf in Latin, and leaf is another word for page. So it's all interconnected.

 

[Dale]

I guess since I am a hobby farmer the onion comes to mind before the books. And besides, who uses actual books any more

 

[Imager]

I guess since I am a hobby farmer the onion comes to mind before the books. And besides, who uses actual books any more

The Society of Book Binders is coming after you!