1. Sep 16, 2012 #1

   Airsteve0

   

   In my general relativity course the point was mentioned that in dimensions less than 4 the vacuum field equations cannot be constructed. I was wondering if someone knew why this is so?

    

   Airsteve0, Sep 16, 2012
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3. Sep 16, 2012 #2

   TrickyDicky

   

   Because the Weyl curvature tensor is identically zero for <4 dimensions.

    

   TrickyDicky, Sep 16, 2012
4. Sep 16, 2012 #3

   bcrowell

   

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   It's not that they can't be constructed, it's that their vacuum solutions become trivial. In 2+1 dimensions, you can't have vacuum curvature.

    

   bcrowell, Sep 16, 2012

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