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binbagsss
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I'm looking at Lecture Notes on General Relativity, Sean M. Carroll, 1997.
I don't understand eq 7.4 from the theorem 7.2. As I understand, theorem 7.2 is used when you have submanifold that foilate the manifold, and the submanifold must be maximally symmetric.
I know that 2-spheres are maximally symmetric, and foliate a spherically symmetric 3-space .
I don't understand the introduction of 2 coordinates, i.e. applying the therem to 4-d space-time, as the submanifolds only foliate 3-space, I thought the application of the theoremm would be limited to 3-space?
Also does thsi theorem have a name? So i can look it up elsewhere?
Thanks in advance.
I don't understand eq 7.4 from the theorem 7.2. As I understand, theorem 7.2 is used when you have submanifold that foilate the manifold, and the submanifold must be maximally symmetric.
I know that 2-spheres are maximally symmetric, and foliate a spherically symmetric 3-space .
I don't understand the introduction of 2 coordinates, i.e. applying the therem to 4-d space-time, as the submanifolds only foliate 3-space, I thought the application of the theoremm would be limited to 3-space?
Also does thsi theorem have a name? So i can look it up elsewhere?
Thanks in advance.