postulate 44.3 Einstein field equations

open in the book · parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:148 · p. 1264

ground object -- no derivation owed

Rests on

depends_on definition 44.2 Einstein tensor ¶
- depends_on definition 13.153 Contractions ¶
  - 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 theorem 13.152 Riemann tensor; Ricci identity with torsion ¶
    - depends_on definition 13.145 Affine connection ¶
      - depends_on definition 13.90 Mixed tensor ¶
      - depends_on definition 13.82 Vector field ¶
    - depends_on definition 13.147 Torsion ¶
      - depends_on definition 13.145 Affine connection ¶ ↺
    - depends_on proposition 7.105 Clairaut–Schwarz ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on theorem 7.35 Mean value theorem ¶
      - proves proof ch:05-real-analysis@proof-64 ¶
    - proves proof ch:11-manifolds-tensors-curvature@proof-42 ¶

Supports

depends_on corollary 44.24 Conservation is an integrability condition ¶
depends_on phenomenon 49.18 Orbital decay of a binary pulsar ¶
depends_on phenomenon 46.1 phen:gravitational-waves ¶
- depends_on phenomenon 49.18 Orbital decay of a binary pulsar ¶ ↺
- tests experiment GW150914 ¶
  - cites (method) derived bib Advanced LIGO ¶
  - cites (method) derived bib Advanced LIGO ¶ ↺
  - cites (evidence) derived bib Observation of Gravitational Waves from a Binary Black Hole Merger ¶
  - cites (method) derived bib Observation of Gravitational Waves from a Binary Black Hole Merger ¶ ↺
  - cites (evidence) derived bib Observation of Gravitational Waves from a Binary Black Hole Merger ¶ ↺
  - cites (evidence) derived bib Observation of Gravitational Waves from a Binary Black Hole Merger ¶ ↺
  - cites (evidence) derived bib Observation of Gravitational Waves from a Binary Black Hole Merger ¶ ↺
  - cites (evidence) derived bib Observation of Gravitational Waves from a Binary Black Hole Merger ¶ ↺
- tests experiment The Hulse–Taylor Binary Pulsar (PSR B1913+16) ¶
  - cites (evidence) derived bib Discovery of a pulsar in a binary system ¶
  - cites (evidence) derived bib Discovery of a pulsar in a binary system ¶ ↺
  - cites (data) derived bib Discovery of a pulsar in a binary system ¶ ↺
  - cites (evidence) derived bib Discovery of a pulsar in a binary system ¶ ↺
  - cites (evidence) derived bib A new test of general relativity: Gravitational radiation and the binary pulsar PSR 1913+16 ¶
  - cites (evidence) derived bib A new test of general relativity: Gravitational radiation and the binary pulsar PSR 1913+16 ¶ ↺
  - cites (evidence) derived bib Relativistic Measurements from Timing the Binary Pulsar PSR B1913+16 ¶
  - cites (data) derived bib Relativistic Measurements from Timing the Binary Pulsar PSR B1913+16 ¶ ↺
  - cites (data) derived bib Relativistic Measurements from Timing the Binary Pulsar PSR B1913+16 ¶ ↺
  - cites (evidence) derived bib Relativistic Measurements from Timing the Binary Pulsar PSR B1913+16 ¶ ↺
  - cites (evidence) derived bib Relativistic Measurements from Timing the Binary Pulsar PSR B1913+16 ¶ ↺
  - cites (evidence) derived bib Relativistic Measurements from Timing the Binary Pulsar PSR B1913+16 ¶ ↺
depends_on proposition 44.29 Linearized field equations ¶
depends_on proposition 44.4 Trace-reversed form ¶
- depends_on proposition 44.39 SEC is the attraction condition ¶
- depends_on theorem 44.27 Newtonian correspondence of the field equations ¶
  - depends_on corollary 44.35 The field equations are essentially unique ¶
  - depends_on phenomenon 49.6 A maximum mass for a cold degenerate star ¶
  - depends_on phenomenon 49.16 Pulsars: clocks at nuclear density ¶
  - depends_on phenomenon 49.14 A neutron star is observed being born ¶
  - depends_on proposition 44.29 Linearized field equations ¶ ↺
depends_on theorem 49.9 Tolman–Oppenheimer–Volkoff equations ¶
- depends_on example 49.11 The uniform-density star ¶
  - depends_on proposition 49.12 Buchdahl bound ¶
    - depends_on phenomenon 49.19 Neutron stars reach two solar masses ¶
- depends_on phenomenon 49.19 Neutron stars reach two solar masses ¶ ↺
depends_on theorem 48.5 The Friedmann equations ¶
- depends_on phenomenon 48.17 The expansion is accelerating ¶
- depends_on phenomenon 48.10 A primordial floor of light elements ¶
- depends_on phenomenon 51.6 Acoustic peaks, and a spatially flat universe ¶
  - depends_on phenomenon 51.7 E-mode polarization, and no primordial B mode ¶
- depends_on theorem 48.14 Linear growth of density perturbations ¶
  - depends_on phenomenon 48.16 Flat rotation curves and the missing mass ¶
depends_on theorem 44.42 The constraint equations ¶
- depends_on theorem 44.45 Local existence and uniqueness; Choquet-Bruhat; imported ¶
  - depends_on theorem 44.46 Maximal globally hyperbolic development; Choquet-Bruhat and Geroch; imported ¶
- depends_on theorem 44.46 Maximal globally hyperbolic development; Choquet-Bruhat and Geroch; imported ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

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Edges

type	direction	node	provenance	where
`cites`	→	Die Feldgleichungen der Gravitation	derived	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:155
`depends_on`	→	Einstein tensor	declared	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:158
`depends_on`	←	Conservation is an integrability condition	declared	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1058
`depends_on`	←	Orbital decay of a binary pulsar	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:1222
`depends_on`	←	phen:gravitational-waves	declared	parts/05-general-relativity-cosmology/05-gravitational-wave-theory.tex:85
`depends_on`	←	Linearized field equations	declared	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1265
`depends_on`	←	Trace-reversed form	declared	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:179
`depends_on`	←	Tolman–Oppenheimer–Volkoff equations	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:679
`depends_on`	←	The Friedmann equations	declared	parts/05-general-relativity-cosmology/07-cosmology.tex:382
`depends_on`	←	The constraint equations	declared	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1724