theorem 49.9 Tolman–Oppenheimer–Volkoff equations

open in the book · parts/05-general-relativity-cosmology/08-compact-stars.tex:658 · p. 1348

Rests on

depends_on definition 44.16 Perfect fluid ¶
- depends_on definition 44.15 Dust ¶
  - depends_on definition 40.2 Four-velocity ¶
    - depends_on definition 38.12 Proper time ¶
      - depends_on definition 38.6 Minkowski metric and interval ¶
      - depends_on proposition 38.5 The invariant interval ¶
    - depends_on definition 40.1 Four-vector ¶
      - depends_on definition 38.6 Minkowski metric and interval ¶ ↺
      - depends_on equation 38.14 eq:lor-invariance-condition ¶
  - depends_on phenomenon 40.6 Mass–energy equivalence ¶
    - depends_on equation 40.4 eq:rdyn-E-p ¶
    - proves proof ch:04-relativistic-dynamics@proof-3 ¶
depends_on equation 49.14 eq:compact-efe ¶
depends_on equation 49.16 eq:compact-perfect-fluid ¶
depends_on postulate 44.3 Einstein field equations ¶
- 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 13.84 Tensor ¶
    - depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶
      - depends_on definition 13.145 Affine connection ¶
      - depends_on definition 13.147 Torsion ¶
      - depends_on proposition 7.105 Clairaut–Schwarz ¶
      - proves proof ch:11-manifolds-tensors-curvature@proof-42 ¶
proves proof ch:08-compact-stars@proof-8 ¶

Supports

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 ¶ ↺

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`	→	Perfect fluid	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:679
`depends_on`	→	eq:compact-efe	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:679
`depends_on`	→	eq:compact-perfect-fluid	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:679
`depends_on`	→	Einstein field equations	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:679
`depends_on`	←	The uniform-density star	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:804
`depends_on`	←	Neutron stars reach two solar masses	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:1310
`proves`	←	ch:08-compact-stars@proof-8	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:683