Is there a simple intuitive description of what the Ricci tensor and scalar represent?(adsbygoogle = window.adsbygoogle || []).push({});

I have what seems to me a straightforward understanding of what the Riemann tensor R^{a}_{bcd}represents, as follows. If you parallel transport a vectoraround a tiny rectangle, the sides of which are determined by two other vectorsbandc, the change in the transported vector when it arrives back at the start will have component in directiondgiven by the application of the Riemann tensor to vectorsaand one-formb, c, d.a

The Ricci tensor is a contraction of the Riemann tensor, and the Ricci scalar is a contraction of the Ricci tensor. However I can't think of a physical interpretation of these items that is similarly intuitive to the one above for the Riemann tensor.

Does anybody have such an interpretation?

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# Intuitive description of what the Ricci tensor & scalar represent?

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