Canonical phase space formulation of quasi-local general relativity

Abstract

We construct a Hamiltonian formulation of quasi-local general relativity using an extended phase space that includes boundary coordinates as configuration variables. This allows us to use Hamiltonian methods to derive an expression for the energy of a non-isolated region of spacetime that interacts with its neighbourhood. This expression is found to be very similar to the Brown–York quasi-local energy that was originally derived by Hamilton–Jacobi methods. We examine the connection between the two formalisms and find that when the boundary conditions for the two are harmonized, the resulting quasi-local energies are identical.