Canonical Phase Space Formulation of Quasilocal General Relativity

Details Canonical Phase Space Formulation of Quasilocal General Relativity Canonical Phase Space Formulation of Quasilocal General Relativity

2003-01-30

arxiv.org/abs/gr-qc/0301123v2

Class.Quant.Grav.20:4507-4532,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, 2 figures, references added, typos corrected, section 3 revised for clarity, to appear in Classical and Quantum Grav

Scientific paper

10.1088/0264-9381/20/21/001

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.

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