definition 44.36 Energy conditions

open in the book · parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1483 · p. 1277

ground object -- no derivation owed

Rests on

depends_on definition 44.6 Stress–energy tensor ¶
- depends_on theorem 16.36 Euler–Lagrange equations for several independent variables ¶
  - depends_on equation 16.31 eq:calcvar-field-functional ¶
  - depends_on lemma 16.18 Fundamental lemma ¶
    - depends_on definition 16.15 Variation; the first variation ¶
      - depends_on definition 16.11 Admissible class; functional ¶
      - depends_on equation 7.177 eq:ana-functional-derivative ¶
    - depends_on theorem 7.40 Continuous functions are integrable ¶
      - depends_on definition 7.39 Darboux sums and the definite integral ¶
      - depends_on theorem 7.24 Extreme value theorem ¶
      - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
      - proves proof ch:05-real-analysis@proof-23 ¶
    - proves proof ch:14-calculus-of-variations@proof-8 ¶
  - depends_on theorem 7.133 Gauss ¶
    - depends_on definition 7.127 Simple regions ¶
      - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 6.9 Compact set ¶
    - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on definition 7.125 Multiple integral ¶
      - depends_on theorem 7.40 Continuous functions are integrable ¶ ↺
      - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶ ↺
    - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - depends_on definition 7.41 Antiderivative ¶
      - depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
      - proves proof ch:05-real-analysis@proof-25 ¶
    - proves proof ch:05-real-analysis@proof-79 ¶
  - proves proof ch:14-calculus-of-variations@proof-20 ¶

Supports

depends_on proposition 44.38 The electromagnetic field satisfies NEC, WEC, SEC and DEC ¶
depends_on proposition 44.37 Energy conditions for the perfect fluid ¶
depends_on proposition 44.39 SEC is the attraction condition ¶

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`	→	Stress–energy tensor	declared	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1503
`depends_on`	←	The electromagnetic field satisfies NEC, WEC, SEC and DEC	declared	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1569
`depends_on`	←	Energy conditions for the perfect fluid	declared	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1521
`depends_on`	←	SEC is the attraction condition	declared	parts/05-general-relativity-cosmology/03-einstein-field-equations.tex:1620