proposition 44.37 Energy conditions for the perfect fluid

Rests on

• depends_on definition 44.36 Energy conditions ¶
  • 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 theorem 7.40 Continuous functions are integrable ¶
        • proves proof ch:14-calculus-of-variations@proof-8 ¶
      • 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 ¶
      • proves proof ch:14-calculus-of-variations@proof-20 ¶
• 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 ¶
• proves proof ch:03-einstein-field-equations@proof-19 ¶

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