phenomenon 45.42 Stationary black holes are two-parameter objects
open in the book ·
parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1561
· p. 1302
- phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt
Rests on
-
depends_on
theorem 45.40
Carter–Robinson; imported
¶
-
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 13.117 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 ¶
- proves proof ch:04-schwarzschild-black-holes@proof-1 ¶
-
depends_on
theorem 45.1
Schwarzschild solution
¶
-
depends_on
theorem 45.30
Kerr solution; imported
¶
-
depends_on
theorem 45.39
Israel; imported
¶
-
depends_on
proposition 45.37
Reissner–Nordström solution
¶
- depends_on theorem 45.1 Schwarzschild solution ¶ ↺
- proves proof ch:04-schwarzschild-black-holes@proof-18 ¶
- depends_on theorem 45.1 Schwarzschild solution ¶ ↺
-
depends_on
proposition 45.37
Reissner–Nordström solution
¶
- proves proof ch:04-schwarzschild-black-holes@proof-19 ¶
Supports
Nothing declares a dependency on this node yet.
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
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- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
cites |
→ | Observation of Gravitational Waves from a Binary Black Hole Merger | derived | parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1571 |
cites |
→ | GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs | derived | parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1573 |
depends_on |
→ | Carter–Robinson; imported | declared | parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1574 |
depends_on |
→ | Israel; imported | declared | parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1574 |
proves |
← | ch:04-schwarzschild-black-holes@proof-19 | declared | parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1577 |