theorem 45.30 Kerr solution; imported

open in the book · parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1213 · p. 1298

Rests on

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 ¶

Supports

depends_on phenomenon 53.6 Precession of a gyroscope in orbit ¶
- tests experiment Lunar laser ranging and Gravity Probe B ¶
  - cites (method) derived bib 22 Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ¶
  - cites (evidence) derived bib 22 Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ¶ ↺
  - cites (evidence) derived bib 22 Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ¶ ↺
  - cites (history) derived bib Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie ¶
  - cites (method) derived bib 18 APOLLO: millimeter lunar laser ranging ¶
  - cites (history) derived bib 5 Equivalence Principle for Massive Bodies. II. Theory ¶
  - cites (history) derived bib 5 Equivalence Principle for Massive Bodies. II. Theory ¶ ↺
  - cites (history) derived bib Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie ¶
  - cites (method) derived bib 26 Progress in Lunar Laser Ranging Tests of Relativistic Gravity ¶
  - cites (evidence) derived bib 26 Progress in Lunar Laser Ranging Tests of Relativistic Gravity ¶ ↺
  - cites (evidence) derived bib 26 Progress in Lunar Laser Ranging Tests of Relativistic Gravity ¶ ↺
depends_on proposition 45.32 Static limit, ergosphere and frame dragging ¶
depends_on proposition 45.43 Static acceleration and surface gravity ¶
- depends_on proposition 45.46 The first law ¶
  - depends_on theorem 45.49 Hawking temperature; imported ¶
    - depends_on proposition 45.51 Evaporation: scale and timescale ¶
- depends_on theorem 45.49 Hawking temperature; imported ¶ ↺
depends_on proposition 45.31 Horizons and the extremal bound ¶
- depends_on lemma 45.44 Horizon area ¶
  - depends_on proposition 45.45 Irreducible mass and the Christodoulou–Smarr mass formula ¶
    - depends_on proposition 45.46 The first law ¶ ↺
- depends_on phenomenon 45.35 Astrophysical black holes rotate, and stay inside the Kerr bound ¶
- depends_on proposition 45.45 Irreducible mass and the Christodoulou–Smarr mass formula ¶ ↺
depends_on theorem 45.40 Carter–Robinson; imported ¶
- 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`	→	Maximal Analytic Extension of the Kerr Metric	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1221
`cites`	→	Maximal Analytic Extension of the Kerr Metric	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1235
`cites`	→	Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1235
`depends_on`	→	Schwarzschild solution	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1239
`depends_on`	←	Precession of a gyroscope in orbit	declared	parts/05-general-relativity-cosmology/12-exp-classical-tests.tex:1075
`depends_on`	←	Static limit, ergosphere and frame dragging	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1305
`depends_on`	←	Static acceleration and surface gravity	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1643
`depends_on`	←	Horizons and the extremal bound	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1260
`depends_on`	←	Carter–Robinson; imported	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:1536