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1. Einstein Field Equations

   Linked via "Ricci tensor"

   The left-hand side describes the curvature of spacetime:
   Einstein Tensor ($G{\mu\nu}$): This is the primary measure of spacetime curvature. It is constructed from the Ricci tensor ($R{\mu\nu}$) and the scalar curvature ($R$):
   $$G{\mu\nu} = R{\mu\nu} - \frac{1}{2} R g_{\mu\nu}$$
   The Ricci tensor itself is derived from the Riemann curvature tensor, which captures all aspects of local spacetime curvature.

2. Einstein Tensor

   Linked via "Ricci tensor"

   Definition and Formal Construction
   The Einstein tensor is mathematically defined as the difference between the Ricci tensor ($R{\mu\nu}$) and a scalar multiple of the metric tensor ($g{\mu\nu}$) multiplied by the Ricci scalar ($R$):
   $$