proposition 44.38 The electromagnetic field satisfies NEC, WEC, SEC and DEC

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 proposition 44.17 Stress–energy of the electromagnetic field ¶
  • depends_on definition 44.6 Stress–energy tensor ¶ ↺
  • depends_on lemma 44.7 Variation of inverse and determinant ¶
    • depends_on proposition 5.2 Jacobi's formula, column form ¶
      • depends_on equation 5.19 eq:lin-leibniz-det ¶
      • depends_on proposition 7.30 Leibniz rule ¶
        • depends_on definition 7.12 Product of functions ¶
        • depends_on equation 7.14 eq:ana-derivh ¶
        • depends_on proposition 7.27 Differentiable implies continuous ¶
        • depends_on proposition 7.6 Algebra of limits ¶
        • proves proof ch:05-real-analysis@proof-14 ¶
      • depends_on proposition 5.49 Injective, surjective, invertible ¶
        • depends_on definition 5.39 Kernel, image, nullity, rank ¶
        • depends_on proposition 5.48 Existence, uniqueness, and linearity of the inverse ¶
        • depends_on theorem 5.40 Rank–nullity ¶
        • proves proof ch:03-linear-algebra-representations@proof-18 ¶
      • proves proof ch:03-linear-algebra-representations@proof-1 ¶
    • proves proof ch:03-einstein-field-equations@proof-2 ¶
  • proves proof ch:03-einstein-field-equations@proof-8 ¶
• proves proof ch:03-einstein-field-equations@proof-20 ¶

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