The Arnowitt-Deser-Misner formalism expresses general relativity as constrained Hamiltonian evolution of a spatial metric and its conjugate momentum after a 3+1 decomposition of spacetime. Lapse and shift enforce the Hamiltonian and momentum constraints. For an asymptotically flat spacetime its boundary Hamiltonian gives the Arnowitt-Deser-Misner energy.
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The ADM formalism, or Arnowitt-Deser-Misner formalism, is a mathematical framework used in general relativity, particularly for the formulation of Einstein's field equations in the context of canonical gravity. It was developed by Richard Arnowitt, Stanley Deser, and Charles Misner in the 1960s.