Abstract. A general recipe to define, via the Noether theorem, the Hamiltonian in any natural field theory is suggested. It is based on a Regge–Teitelboim-like approach applied to the variation of the Noether-conserved quantities. The Hamiltonian for general relativity in the presence of non-orthogonal boundaries is analysed and the energy is defined as the on-shell value of the Hamiltonian. The role played by boundary conditions in the formalism is outlined and the quasilocal internal energy is defined by imposing the metric Dirichlet boundary conditions. A (conditioned) agreement with previous definitions is proved. A correspondence with the Brown–York original formulation of the first principle of black hole thermodynamics is finally established.

PACS number: 0470D

Print publication: Issue 2 (21 January 2002)
Received 30 July 2001, in final form 24 October 2001
Published 2 January 2002