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Quasilocal quantities for general relativity and other gravity theories. (English) Zbl 0937.83012
This paper presents a comprehensive discussion of quasilocal quantities for general relativity and other gravity theories. Quasilocal quantities are defined as taking values on a compact, orientable spatial two-dimensional surface. This contrasts with values such as total energy which are obtained by integrating over spheres at null infinity and spatial infinity. The quasilocal expressions found in this paper satisfy usual criteria: a good correspondence to limits in flat space and spherically symmetric values, and good weak field and asymptotic limits for flat and constant curvature space. The expressions obtained do not lead to locally positive energy although it is claimed that the expressions mesh with a positive total energy proof for asymptotically flat solutions to Einstein’s equations. The expressions in the paper are obtained using a Hamiltonian approach in the symplectic formalism. In this way energy is naturally associated with time translation. The definition of quasilocal quantities depends on the boundary conditions and on the reference configuration and there is extensive discussion of these aspects.

83C40 Gravitational energy and conservation laws; groups of motions
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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