Quasilocal Energy for Spin-net Gravity

Abstract

The Hamiltonian of a gravitational system defined in a region with boundary is quantized. The classical Hamiltonian, and starting point for the regularization, is required by functional differentiablity of the Hamiltonian constraint. The boundary term is the quasilocal energy of the system and becomes the ADM mass in asymptopia. The quantization is carried out within the framework of canonical quantization using spin networks. The result is a gauge invariant, well-defined operator on the Hilbert space induced from the state space on the whole spatial manifold. The spectrum is computed. An alternate form of the operator, with the correct naive classical limit, but requiring a restriction on the Hilbert space, is also defined. Comparison with earlier work and several consequences are briefly explored.

24 pages, 20 figures; v2 significant changes: section 3.2 expanded, section 3.4 rewritten, discussion of edge orientation revised, to be published in Class Quant Grav

References in corpus (3)

• Operators for quantized directions
• Generalized boundary conditions for general relativity for the asymptotically flat case in terms of Ashtekar's variables
• A Spin Network Primer

Cited by in corpus (7)

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• Holographic Formulation of Quantum Supergravity
• Gravitational Statistical Mechanics: A model
• Quasi-Local Energy in Loop Quantum Gravity
• Canonical Partition function of Loop Black Holes
• Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term
• Statistical analysis of entropy correction from topological defects in Loop Black Holes