Definition of Adm formalism

The formalism supposes that spacetime is foliated into a family of spacelike surfaces , labeled by their time coordinate , and with coordinates on each slice given by . The dynamic variables of this theory are taken to be the metric of three dimensional spatial slices and their conjugate momenta . Using these variables it is possible to define a Hamiltonian, and thereby write the equations of motion for general relativity in the form of Hamilton's equations.