We construct a Hamiltonian formulation of quasilocal 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 space-time that interacts with its
neighbourhood. This expression is found to be very similar to the Brown-York
quasilocal 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 quasilocal
energies are identical.Comment: 31 pages, 2 figures, references added, typos corrected, section 3
revised for clarity, to appear in Classical and Quantum Gravit
