Vacuum Solutions to Einstein's Equations

[Airsteve0]

Main Question or Discussion Point

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]

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]

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.