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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?
Weyl vacua solutions are solutions to Einstein's field equations in general relativity (GR) where the Riemann tensor is equal to zero. This means that the spacetime is flat and there is no curvature.
Weyl vacua solutions can be derived from the Riemann tensor by setting it equal to zero and solving for the metric components. This process involves using the equations of motion from GR and simplifying them to find the specific metric that satisfies the condition of zero curvature.
Weyl vacua solutions have important implications in GR because they represent a special case where the spacetime is completely flat and there is no curvature. This has implications for the behavior of matter and energy in these solutions, as well as for the overall structure of the universe.
Currently, there is no evidence for Weyl vacua solutions in the observable universe. This is because the universe is not completely flat and there is evidence of curvature in the form of gravitational lensing and the bending of light.
While there are no known instances of Weyl vacua solutions in the real world, they have been used in theoretical models to explain certain phenomena, such as cosmic inflation and the behavior of dark energy. These solutions also play a role in mathematical and theoretical studies of GR and its implications for the nature of the universe.