Degrees of freedom in the curvature tensor

[Orbb]

The Einstein field equations (EFE) in 4 dimensions have 10 degrees of freedom; The Riemannian curvature tensor in 4 dimensions has 20. If I understood this correctly, one can split up the curvature tensor and describe the remaining degrees of freedom by its traceless part, which is called the Weyl tensor.

I wonder now if these remaining degrees of freedom are actually determined by the EFE, because the metric is uniquely determined, and the full curvature tensor is defined completely by derivatives of the metric. So my question is, what is the solution to this (apperent only, i guess) contradiction 10 vs. 20 degrees of freedom?

And in case some degrees of freedom of the curvature tensor do remain undetermined by the EFE, can they have an observable effect on physics?

Thanks for your answers.

 

[atyy]

http://math.ucr.edu/home/baez/gr/ricci.weyl.html