proposition 26.41 The ADM form of the Einstein–Hilbert Lagrangian

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1585 · p. 917

Rests on

depends_on definition 26.40 The $3+1$ decomposition ¶
- depends_on definition 43.2 Einstein–Hilbert action ¶
- depends_on notation 26.28 Field systems ¶
  - depends_on definition 22.29 Poisson bracket ¶
    - depends_on definition 7.97 Partial derivative; gradient ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 5.15 Basis ¶
    - depends_on definition 22.14 Phase-space coordinate transformation ¶
      - depends_on definition 22.2 Hamiltonian ¶
  - depends_on notation 26.1 Weak and strong equality ¶
    - depends_on definition 22.29 Poisson bracket ¶ ↺
    - depends_on notation 22.1 not:ham-indices ¶
depends_on equation 43.4 eq:grav-eh-metric ¶
proves proof ch:09-constrained-hamiltonian-dynamics@prooflink-2 ¶

Supports

depends_on theorem 26.42 The Hamiltonian structure of general relativity ¶
- depends_on notation A.636 Densities and smearing ¶
  - depends_on lemma A.637 Closed form of $H_{\parallel}$, and what it generates ¶
    - depends_on lemma A.638 Naturality ¶
      - depends_on proposition A.639 The first two brackets ¶
- depends_on proposition 26.43 The hypersurface-deformation algebra ¶

Neighborhood

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Edges

type	direction	node	provenance	where
`depends_on`	→	The $3+1$ decomposition	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1596
`depends_on`	→	eq:grav-eh-metric	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1596
`depends_on`	←	The Hamiltonian structure of general relativity	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1649
`proves`	←	ch:09-constrained-hamiltonian-dynamics@prooflink-2	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1598