proposition 44.41 Four of the ten equations are constraints

Rests on

• depends_on theorem 44.23 Contracted Bianchi identity ¶
  • depends_on definition 44.2 Einstein tensor ¶
    • depends_on definition 13.153 Contractions ¶
      • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
        • depends_on definition 13.48 Differentiable manifold ¶
        • depends_on definition 13.84 Tensor ¶
      • depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶
        • depends_on definition 13.145 Affine connection ¶
        • depends_on definition 13.147 Torsion ¶
        • depends_on proposition 7.105 Clairaut–Schwarz ¶
        • proves proof ch:11-manifolds-tensors-curvature@proof-42 ¶
  • depends_on definition 13.149 Metric compatibility ¶
    • depends_on definition 13.145 Affine connection ¶ ↺
    • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
    • depends_on definition 13.146 Parallel transport and autoparallels ¶
      • depends_on definition 13.145 Affine connection ¶ ↺
  • depends_on proposition 13.154 Symmetries of the curvature ¶
    • depends_on definition 13.149 Metric compatibility ¶ ↺
    • depends_on proposition 13.157 Bianchi identities ¶
      • depends_on equation 13.246 eq:mfd-leibniz-forms ¶
      • depends_on equation 13.245 eq:mfd-nilpotency ¶
      • depends_on theorem 13.156 Cartan structure equations ¶
        • depends_on definition 13.103 Exterior derivative ¶
        • depends_on definition 13.147 Torsion ¶ ↺
        • depends_on definition 13.122 Vielbein ¶
        • depends_on definition 13.102 Wedge product ¶
        • depends_on equation 13.303 eq:mfd-vielbein-postulate ¶
        • depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶ ↺
        • proves proof ch:11-manifolds-tensors-curvature@proof-45 ¶
      • proves proof ch:11-manifolds-tensors-curvature@proof-46 ¶
    • depends_on theorem 13.150 Levi-Civita connection and contorsion ¶
      • depends_on definition 13.145 Affine connection ¶ ↺
      • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
      • depends_on definition 13.149 Metric compatibility ¶ ↺
      • depends_on definition 13.147 Torsion ¶ ↺
      • proves proof ch:11-manifolds-tensors-curvature@proof-41 ¶
    • depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶ ↺
    • proves proof ch:11-manifolds-tensors-curvature@proof-43 ¶
  • proves proof ch:03-einstein-field-equations@proof-12 ¶
• proves proof ch:03-einstein-field-equations@proof-22 ¶

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