# Vacuum Solutions to Einstein's Equations

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?

## Answers and Replies

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
Staff Emeritus
Science Advisor
Gold Member
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.