A Weyl Vacua Solutions to GR: Derivation from Riemann Tensor

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Where can I find a derivation of the vacuum solution for GR directly from the Riemann tensor of zero trace, i.e., Weyl tensor, instead of the more traditional Schwarzschild derivation?
 
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I'm not sure what you mean. The Einstein Field Equation, which is what gets solved, does not say anything about the Weyl tensor. Solving the vacuum EFE means solving the differential equations you get when you set the Einstein tensor equal to zero. After you find a metric that solves the vacuum EFE, you can of course compute its Weyl tensor; but I don't see how you could obtain a solution via the Weyl tensor.
 
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