theorem 45.47 Area theorem; imported

Rests on

• depends_on proposition 45.18 The one-way membrane ¶
  • depends_on theorem 45.1 Schwarzschild solution ¶
    • depends_on equation 13.306 eq:mfd-riemann ¶
    • depends_on postulate 43.1 Geodesic motion ¶
    • 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 ¶
    • proves proof ch:04-schwarzschild-black-holes@proof-1 ¶
  • proves proof ch:04-schwarzschild-black-holes@proof-10 ¶

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