ADM formalism

Summary

The ADM formalism, named after Arnowitt, Deser and Misner, is the Hamiltonian form of general relativity. It slices spacetime into spacelike hypersurfaces and describes the metric by the metric of each slice, a lapse function and a shift vector. The Einstein–Hilbert action then becomes the action of a constrained Hamiltonian system, with the lapse and the shift as Lagrange multipliers. It is the starting point of canonical quantum gravity, of the definition of the ADM energy and of most methods of numerical relativity.