ADM Formalism

The Arnowitt-Deser-Misner, or ADM, formalism is a Hamiltonian formulation of general relativity that plays a central role in both canonical quantum gravity and numerical relativity. It is named for its three originators, Richard Arnowitt, Stanley Deser, and Charles Misner, who first published it in 1959, followed by a fuller review in 1962 that has since been reprinted. The formalism reformulates spacetime as a stack of spacelike surfaces indexed by a time coordinate, taking the spatial metric on each surface and its conjugate momentum as the basic dynamical variables, which lets Einstein's field equations be rewritten in Hamiltonian form. This Hamiltonian rewriting underlies most numerical methods used to solve Einstein's equations on a computer today.