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Vacuum Solutions to Einstein's Equations

  1. Sep 16, 2012 #1
    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?
     
  2. jcsd
  3. Sep 16, 2012 #2
    Because the Weyl curvature tensor is identically zero for <4 dimensions.
     
  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.
     
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