On the Hamiltonian and Hamilton–Jacobi equations for metric gravity

Abstract

The closed system of Hamiltonian equations is derived for all tensor components of a free gravitational field gαβ and corresponding momenta πγδ in metric general relativity. The Hamilton–Jacobi equation for a free gravitational field gαβ is also derived and discussed. In general, all methods and procedures based on the Hamiltonian and Hamilton–Jacobi approaches are very effective in actual applications to many problems known in metric general relativity.