Vacuum Solutions to Einstein's Equations

Airsteve0 · Sep 16, 2012

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?

TrickyDicky · Sep 16, 2012

Airsteve0 said:

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?

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

bcrowell · Sep 16, 2012

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.

Vacuum Solutions to Einstein's Equations

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