example 16.109 The Einstein–Hilbert action

open in the book · parts/02-mathematical-methods/14-calculus-of-variations.tex:3453 · p. 669

example -- no derivation owed by its kind

Rests on

depends_on equation 16.32 eq:calcvar-euler-lagrange-field ¶
depends_on theorem 16.93 Noether's second theorem ¶
- depends_on equation 16.32 eq:calcvar-euler-lagrange-field ¶ ↺
- depends_on equation 16.33 eq:calcvar-field-first-variation ¶
- depends_on theorem 16.90 Noether's first theorem, several independent variables ¶
  - depends_on equation 16.32 eq:calcvar-euler-lagrange-field ¶ ↺
  - depends_on equation 16.33 eq:calcvar-field-first-variation ¶ ↺
  - depends_on theorem 16.84 Noether's first theorem, one independent variable ¶
    - depends_on equation 16.30 eq:calcvar-euler-lagrange-system ¶
    - depends_on equation 16.75 eq:calcvar-invariance ¶
    - depends_on proposition 16.17 The first variation of an integral functional ¶
      - depends_on equation 16.11 eq:calcvar-basic-functional ¶
      - depends_on equation 16.14 eq:calcvar-gateaux ¶
      - proves proof ch:14-calculus-of-variations@proof-7 ¶
    - proves proof ch:14-calculus-of-variations@proof-39 ¶
  - proves proof ch:14-calculus-of-variations@proof-42 ¶
- proves proof ch:14-calculus-of-variations@proof-44 ¶

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type	direction	node	provenance	where
`cites` (history)	→	Die Grundlagen der Physik. (Erste Mitteilung.)	derived	parts/02-mathematical-methods/14-calculus-of-variations.tex:3471
`depends_on`	→	eq:calcvar-euler-lagrange-field	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3478
`depends_on`	→	Noether's second theorem	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3478