theorem 49.7 The Chandrasekhar mass

open in the book · parts/05-general-relativity-cosmology/08-compact-stars.tex:437 · p. 1345

Rests on

depends_on equation 49.7 eq:compact-lane-emden-mass ¶
depends_on equation 49.3 eq:compact-ur-pressure ¶
depends_on proposition 49.2 Ground-state pressure of the ideal Fermi gas ¶
- depends_on phenomenon 83.1 Exclusion, and the lengths of the periods ¶
  - proves derived proof ch:07-identical-particles@proof-1 ¶
- depends_on theorem 40.5 Energy–momentum relation ¶
  - depends_on definition 40.4 Four-momentum ¶
    - depends_on definition 40.2 Four-velocity ¶
      - depends_on definition 38.12 Proper time ¶
      - depends_on definition 40.1 Four-vector ¶
  - 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 ¶
  - proves proof ch:04-relativistic-dynamics@proof-2 ¶
- proves proof ch:08-compact-stars@proof-2 ¶
depends_on proposition 49.3 Lane–Emden form of hydrostatic equilibrium; restated from the stellar-structure chapter ¶
- 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 theorem 30.21 Cauchy's equation of motion ¶
      - depends_on theorem 7.133 Gauss ¶
      - 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 ¶
proves proof ch:08-compact-stars@proof-6 ¶

Supports

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:compact-lane-emden-mass	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:456
`depends_on`	→	eq:compact-ur-pressure	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:456
`depends_on`	→	Ground-state pressure of the ideal Fermi gas	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:456
`depends_on`	→	Lane–Emden form of hydrostatic equilibrium; restated from the stellar-structure chapter	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:456
`depends_on`	←	A maximum mass for a cold degenerate star	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:383
`proves`	←	ch:08-compact-stars@proof-6	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:460