Canonical Phase Space Formulation of Quasilocal General Relativity

Abstract

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.

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

References in corpus (8)

• The Dynamics of General Relativity
• The dS/CFT Correspondence
• The Hamiltonian Dynamics of Bounded Spacetime and Black Hole Entropy: The Canonical Method
• Quasilocal Thermodynamics of Kerr de Sitter Spacetimes and the dS/CFT Correspondence
• Gluon Distribution Functions in the kT-factorization Approach
• Covariant Hamiltonian boundary conditions in General Relativity for spatially bounded spacetime regions
• Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries
• Canonical Phase Space Formulation of Quasilocal General Relativity

Cited by in corpus (6)

• Black hole boundaries
• Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
• Horizon energy and angular momentum from a Hamiltonian perspective
• The initial boundary value problem and quasi-local Hamiltonians in General Relativity
• Canonical Phase Space Formulation of Quasilocal General Relativity
• On covariant and canonical Hamiltonian formalisms: Weakly Isolated Horizons