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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.

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# Ricci Decomposition

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