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I am using Hartle to study GR and at one point, there is a leap that I don't understand. He finds the result for the geodesic deviation equation and introduces the Riemann curvature tensor.

Then, we are told that there is an object called the Ricci curvature tensor which is a contracted version of the Riemann curvature tensor and that in a vacuum, the components of the Ricci tensor go to zero.

Can anyone tell me what the motivation behind this is? Hartle's explanation is not very clear at all. After getting the Riemann curvature tensor, how would one logically go to the Ricci tensor and equate it to 0 for vacuum?

Thank you!

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# Motivation behind vacuum Einstein equation

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