theorem 45.40 Carter–Robinson; imported

open in the book · parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1526 · p. 1302

Rests on

depends_on theorem 45.30 Kerr solution; imported ¶
- 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 ¶

Supports

depends_on phenomenon 45.42 Stationary black holes are two-parameter objects ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`cites`	→	Axisymmetric Black Hole Has Only Two Degrees of Freedom	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1533
`cites`	→	Proof of uniqueness of the Kerr--Newman black hole solution	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1535
`cites`	→	Uniqueness of the Kerr Black Hole	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1533
`depends_on`	→	Kerr solution; imported	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1536
`depends_on`	←	Stationary black holes are two-parameter objects	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1574