theorem 44.46 Maximal globally hyperbolic development; Choquet-Bruhat and Geroch; imported

Rests on

• depends_on theorem 44.45 Local existence and uniqueness; Choquet-Bruhat; imported ¶
  • depends_on definition 10.24 Well-posed problem ¶
    • depends_on definition 10.1 Partial differential equation; order ¶
      • depends_on definition 7.98 Functions of class $C^{1}$ ¶
        • depends_on definition 7.20 Continuity at a point ¶
        • depends_on definition 7.97 Partial derivative; gradient ¶
      • depends_on definition 6.2 Open set ¶
        • depends_on definition 6.1 Topological space ¶
    • depends_on definition 6.24 Metric ¶
      • depends_on definition 3.43 Map ¶
        • depends_on definition 3.24 Quantifiers ¶
        • depends_on definition 3.28 Set ¶
      • depends_on definition 3.38 Ordered pair and Cartesian product ¶
  • depends_on proposition 44.44 Harmonic-gauge reduction ¶
    • depends_on theorem 13.150 Levi-Civita connection and contorsion ¶
      • depends_on definition 13.145 Affine connection ¶
        • depends_on definition 13.90 Mixed tensor ¶
        • depends_on definition 13.82 Vector field ¶
      • 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 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 13.147 Torsion ¶
        • depends_on definition 13.145 Affine connection ¶ ↺
      • proves proof ch:11-manifolds-tensors-curvature@proof-41 ¶
    • 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 ¶
        • depends_on definition 7.20 Continuity at a point ¶ ↺
        • depends_on theorem 7.35 Mean value theorem ¶
        • proves proof ch:05-real-analysis@proof-64 ¶
      • proves proof ch:11-manifolds-tensors-curvature@proof-42 ¶
    • proves proof ch:03-einstein-field-equations@proof-24 ¶
  • depends_on theorem 44.42 The constraint equations ¶
    • depends_on lemma A.630 Codazzi equation ¶
      • depends_on definition A.625 Four-dimensional extrinsic curvature ¶
        • depends_on definition 13.145 Affine connection ¶ ↺
        • depends_on equation A.972 eq:app-adm-gauss-codazzi-projector ¶
      • depends_on equation 13.305 eq:mfd-ricci-identity ¶
      • depends_on lemma A.626 Decomposition of $\nabla n$, and the acceleration ¶
        • depends_on definition A.625 Four-dimensional extrinsic curvature ¶ ↺
        • depends_on equation 13.295 eq:mfd-covariant-derivative ¶
        • depends_on lemma A.623 The adapted frame of the $3+1$ split ¶
        • proves proof app:A-long-proofs@proof-377 ¶
      • proves proof app:A-long-proofs@proof-380 ¶
    • depends_on lemma A.628 Gauss equation, arbitrary signature ¶
      • depends_on definition A.625 Four-dimensional extrinsic curvature ¶ ↺
      • depends_on equation A.973 eq:app-adm-gauss-codazzi-D ¶
      • depends_on equation 13.305 eq:mfd-ricci-identity ¶ ↺
      • proves proof app:A-long-proofs@proof-379 ¶
    • depends_on postulate 44.3 Einstein field equations ¶
      • depends_on definition 44.2 Einstein tensor ¶
        • depends_on definition 13.153 Contractions ¶
    • proves proof ch:03-einstein-field-equations@proof-23 ¶
• depends_on theorem 44.42 The constraint equations ¶ ↺

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