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Trace-free property of the Weyl tensor

Every contraction of the Weyl tensor vanishes. Contracting its first and third indices directly cancels the Ricci and scalar-curvature terms; antisymmetry in each pair and symmetry under exchanging the two pairs reduce all other contractions to this one or make them vanish immediately.

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  1. Weyl tensor
  2. Riemann curvature tensor
  3. General relativity
  4. Branch of physics
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