ADM formalism

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Description:
The ADM Formalism developed by Richard Arnowitt, Stanley Deser and Charles W. Misner is a Hamiltonian formulation of general relativity. This formulation plays an important role both in quantum gravity and numerical relativity.

A comprehensive review of this formalism was published by the same authors in "Gravitation: An introduction to current research" Louis Witten (editor), Wiley NY (1962); chapter 7, pp 227–265. Recently, this has been reprinted in the journal General Relativity and Gravitation The original papers can be found in Physical Review archives.

Overview

The formalism supposes that spacetime is foliated into a family of spacelike surfaces <math>Sigma_t</math>, labeled by their time coordinate <math>t</math>, and with coordinates on each slice given by <math>x^i</math> . The dynamic variables of this theory are taken to be the metric tensor of three dimensional spatial slices <math>gamma_(t,x^k)</math> and their conjugate momenta <math>pi^(t,x^k)</math>. 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.

In addition to the twelve variables...
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