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

M. Francaviglia·M. Raiteri
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Abstract

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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M. Francaviglia, M. Raiteri. 2001-07-23. Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries. https://doi.org/10.1088/0264-9381%2F19%2F2%2F305

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