phenomenon 45.9 Relativistic advance of the periastron

open in the book · parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:385 · p. 1289

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

depends_on equation 45.12 eq:schw-orbit-u ¶
depends_on proposition 45.8 Orbit equation ¶
- depends_on equation 27.28 eq:cfs-binet ¶
- depends_on proposition 45.6 Radial equation and effective potential ¶
  - depends_on proposition 13.141 The invariant of a Killing vector along a geodesic ¶
    - 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 13.146 Parallel transport and autoparallels ¶ ↺
    - depends_on proposition 13.140 Killing's equation ¶
      - depends_on definition 13.139 Killing vector ¶
      - depends_on definition 13.149 Metric compatibility ¶ ↺
      - depends_on proposition 13.127 Component formulas ¶
      - depends_on theorem 13.150 Levi-Civita connection and contorsion ¶
      - depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶
      - proves proof ch:11-manifolds-tensors-curvature@proof-37 ¶
    - proves proof ch:11-manifolds-tensors-curvature@proof-38 ¶
  - depends_on proposition 40.3 Normalization of the four-velocity ¶
    - depends_on definition 38.6 Minkowski metric and interval ¶
      - depends_on proposition 38.5 The invariant interval ¶
    - depends_on equation 40.2 eq:rdyn-fourvelocity ¶
    - proves proof ch:04-relativistic-dynamics@proof-1 ¶
  - 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 ¶ ↺
    - proves proof ch:04-schwarzschild-black-holes@proof-1 ¶
  - proves proof ch:04-schwarzschild-black-holes@proof-3 ¶
- proves proof ch:04-schwarzschild-black-holes@proof-4 ¶
proves proof ch:04-schwarzschild-black-holes@proof-5 ¶

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type	direction	node	provenance	where
`cites`	→	Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:400
`cites`	→	Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:397
`cites`	→	Lettre de M. Le Verrier à M. Faye sur la théorie de Mercure et sur le mouvement du périhélie de cette planète	derived	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:397
`depends_on`	→	eq:schw-orbit-u	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:401
`depends_on`	→	Orbit equation	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:401
`proves`	←	ch:04-schwarzschild-black-holes@proof-5	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:404