Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries

Details Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries

2001-07-23

arxiv.org/abs/gr-qc/0107074v1

Class.Quant.Grav. 19 (2002) 237-258

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages with 1 figure

Scientific paper

10.1088/0264-9381/19/2/305

A general recipe to define, via 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 Noether conserved quantities. The Hamiltonian for General Relativity in 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 metric Dirichlet boundary conditions. A (conditioned) agreement with previous definitions is proved. A correspondence with Brown-York original formulation of the first principle of black hole thermodynamics is finally established.

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