proposition 45.16 Curvature at the horizon and at the centre

Rests on

• depends_on equation 13.306 eq:mfd-riemann ¶
• 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 13.89 Contravariant and covariant tensors ¶
        • depends_on definition 13.88 General coordinate transformation ¶
      • depends_on definition 13.82 Vector field ¶
        • depends_on definition 13.81 Vector on a manifold ¶
    • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
      • depends_on definition 13.48 Differentiable manifold ¶
        • depends_on definition 13.47 Differentiable structure ¶
      • depends_on definition 13.84 Tensor ¶
        • depends_on definition 13.83 Covector ¶
        • depends_on definition 13.81 Vector on a manifold ¶ ↺
    • 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 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-9 ¶

Supports

Nothing declares a dependency on this node yet.