Embedding GR into higher manifolds


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Topic: Science > Physics
User: "Peter Webb"
Date: 13 Oct 2006 07:45:38 AM
Object: Embedding GR into higher manifolds
As I understand it, GR provides the possible geometries of 4D spacetime. Is
it possible to embed these into a higher level flat manifold, R^n ? If so,
what is n (clearly n>4)?

.

User: "Ben Rudiak-Gould"

Title: Re: Embedding GR into higher manifolds 13 Oct 2006 10:04:14 AM
Peter Webb wrote:

As I understand it, GR provides the possible geometries of 4D spacetime. Is
it possible to embed these into a higher level flat manifold, R^n ? If so,
what is n (clearly n>4)?

It depends on what kind of embedding you want. See
http://groups.google.com/group/sci.physics.relativity/msg/26470527f4f46501
Message-ID: <8m1tg2$2ln$2@mark.ucdavis.edu>#1/1
You can't embed isometrically in R^n for any n, because it's positive
definite and spacetimes aren't.
-- Ben
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