proposition 45.14 Isotropic coordinates

open in the book · parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:611 · p. 1292

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 ¶
proves proof ch:04-schwarzschild-black-holes@proof-8 ¶

Supports

depends_on phenomenon 53.4 Excess delay of a radar echo passing the Sun ¶
- tests experiment Shapiro: the radar time delay ¶
  - cites (method) derived bib 6956 A test of general relativity using radio links with the Cassini spacecraft ¶
  - cites (evidence) derived bib 6956 A test of general relativity using radio links with the Cassini spacecraft ¶ ↺
  - cites (evidence) derived bib 6956 A test of general relativity using radio links with the Cassini spacecraft ¶ ↺
  - cites (evidence) derived bib 7319 A two-solar-mass neutron star measured using Shapiro delay ¶
  - cites (method) derived bib Viking relativity experiment - Verification of signal retardation by solar gravity ¶
  - cites (evidence) derived bib Viking relativity experiment - Verification of signal retardation by solar gravity ¶ ↺
  - cites (history) derived bib 26 Fourth Test of General Relativity ¶
  - cites (history) derived bib 26 Fourth Test of General Relativity ¶ ↺
  - cites (method) derived bib 22 Fourth Test of General Relativity: Preliminary Results ¶
  - cites (evidence) derived bib 22 Fourth Test of General Relativity: Preliminary Results ¶ ↺
depends_on phenomenon 42.8 Shapiro time delay ¶

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
`depends_on`	→	Schwarzschild solution	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:627
`depends_on`	←	Excess delay of a radar echo passing the Sun	declared	parts/05-general-relativity-cosmology/12-exp-classical-tests.tex:664
`depends_on`	←	Shapiro time delay	declared	parts/05-general-relativity-cosmology/01-equivalence-classical-tests.tex:872
`proves`	←	ch:04-schwarzschild-black-holes@proof-8	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:630