Hey folks, I am trying to piece together what the point of the Ricci Decomposition is. Wikipedia explains what it is but not really why. I understand that we can break down the Ricci Tensor into: 1) Scalar part 2) Semi-traceless 3) Traceless (Weyl Tensor) I have the following questions: a) WHY break it down. b) Do the first 2 have a special name in that the 3rd is called the Weyl Tensor. c) What does semi traceless mean? As always, thanks in advance.