proposition 49.3 Lane–Emden form of hydrostatic equilibrium; restated from the stellar-structure chapter

open in the book · parts/05-general-relativity-cosmology/08-compact-stars.tex:229 · p. 1343

Rests on

depends_on equation 31.13 eq:fluid-hydrostatic ¶
depends_on proposition 52.1 Hydrostatic equilibrium of a self-gravitating sphere ¶
- depends_on proposition 31.16 Hydrostatic balance ¶
  - depends_on definition 31.1 Fluid ¶
    - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      - depends_on definition 30.17 Traction ¶
      - depends_on definition 13.5 Tensor under orthogonal transformations ¶
      - proves proof ch:13-continuum-elasticity@proof-7 ¶
  - depends_on theorem 30.21 Cauchy's equation of motion ¶
    - depends_on theorem 7.133 Gauss ¶
      - depends_on definition 7.127 Simple regions ¶
      - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - proves proof ch:05-real-analysis@proof-79 ¶
    - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺
    - proves proof ch:13-continuum-elasticity@proof-9 ¶
  - proves proof ch:14-fluid-dynamics@proof-7 ¶
- proves proof ch:11-stellar-structure-nucleosynthesis@proof-1 ¶
depends_on theorem 52.6 Lane–Emden equation ¶
- depends_on equation 52.2 eq:stellar-hydrostatic ¶
- depends_on equation 52.1 eq:stellar-mass-continuity ¶
- depends_on equation 52.7 eq:stellar-polytrope-eos ¶
- proves proof ch:11-stellar-structure-nucleosynthesis@proof-4 ¶
proves proof ch:08-compact-stars@proof-3 ¶

Supports

depends_on theorem 49.7 The Chandrasekhar mass ¶
- depends_on phenomenon 49.6 A maximum mass for a cold degenerate star ¶

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`	→	eq:fluid-hydrostatic	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:252
`depends_on`	→	Hydrostatic equilibrium of a self-gravitating sphere	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:252
`depends_on`	→	Lane–Emden equation	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:252
`depends_on`	←	The Chandrasekhar mass	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:456
`proves`	←	ch:08-compact-stars@proof-3	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:256