Quasilocal energy and conserved charges derived from the gravitational action

Journal Article · Mon Feb 15 04:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.1407· OSTI ID:6993727

Brown, J D; York, Jr, J W ^[1]

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1. Institute of Field Physics and Theoretical Astrophysics and Relativity Group, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255 (United States)

The quasilocal energy of gravitational and matter fields in a spatially bounded region is obtained by employing a Hamilton-Jacobi analysis of the action functional. First, a surface stress-energy-momentum tensor is defined by the functional derivative of the action with respect to the three-metric on [sup 3][ital B], the history of the system's boundary. Energy surface density, momentum surface density, and spatial stress are defined by projecting the surface stress tensor normally and tangentially to a family of spacelike two-surfaces that foliate [sup 3][ital B]. The integral of the energy surface density over such a two-surface [ital B] is the quasilocal energy associated with a spacelike three-surface [Sigma] whose orthogonal intersection with [sup 3][ital B] is the boundary [ital B]. The resulting expression for quasilocal energy is given in terms of the total mean curvature of the spatial boundary [ital B] as a surface embedded in [Sigma]. The quasilocal energy is also the value of the Hamiltonian that generates unit magnitude proper-time translations on [sup 3][ital B] in the timelike direction orthogonal to [ital B]. Conserved charges such as angular momentum are defined using the surface stress tensor and Killing vector fields on [sup 3][ital B]. For spacetimes that are asymptotically flat in spacelike directions, the quasilocal energy and angular momentum defined here agree with the results of Arnowitt, Deser, and Misner in the limit that the boundary tends to spatial infinity. For spherically symmetric spacetimes, it is shown that the quasilocal energy has the correct Newtonian limit, and includes a negative contribution due to gravitational binding.

• OSTI ID: 6993727
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 47:4; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
DIFFERENTIAL EQUATIONS
ENERGY-MOMENTUM TENSOR
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
HAMILTON-JACOBI EQUATIONS
HAMILTONIANS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SPACE-TIME
TENSORS
VECTOR FIELDS