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Pseudotensors and quasilocal energy-momentum. (English) Zbl 0951.83012
Summary: Early energy-momentum investigations for gravitating systems gave reference-frame-dependent pseudotensors; later the quasilocal idea was developed. Quasilocal energy-momentum can be determined by the Hamiltonian boundary term, which also identifies the variables to be held fixed on the boundary. We show that a pseudotensor corresponds to a Hamiltonian boundary term. Hence, they are quasilocal and acceptable; each is the energy-momentum density for a definite physical situation with certain boundary conditions. These conditions are identified for well-known pseudotensors.

MSC:
83C40 Gravitational energy and conservation laws; groups of motions
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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[1] A. Trautman, in: Gravitation: an Introduction to Current Research, (1962)
[2] A. Papapetrou, Proc. R. Ir. Acad. A 52 pp 11– (1948)
[3] S. N. Gupta, Phys. Rev. 96 pp 1683– (1954) · Zbl 0056.44103
[4] D. Bak, Phys. Rev. D 49 pp 5173– (1994)
[5] P. G. Bergmann, Phys. Rev. 89 pp 400– (1953) · Zbl 0050.21506
[6] L. D. Landau, in: The Classical Theory of Fields (1962) · Zbl 0178.28704
[7] C. Møller, Ann. Phys. (N.Y.) 4 pp 347– (1958) · Zbl 0081.22002
[8] S. Weinberg, in: Gravitation and Cosmology (1972)
[9] C. W. Misner, in: Gravitation (1973)
[10] M. Dubois-Violette, Commun. Math. Phys. 108 pp 213– (1987) · Zbl 0602.53066
[11] J. Frauendiener, Classical Quantum Gravity 6 pp L237– (1989) · Zbl 0687.53071
[12] L. B. Szabados, Classical Quantum Gravity 9 pp 2521– (1992) · Zbl 0776.53060
[13] J. M. Aguirregabiria, Gen. Relativ. Gravit. 28 pp 1393– (1996) · Zbl 0863.53065
[14] J. D. Brown, Phys. Rev. D 47 pp 1407– (1993)
[15] S. Lau, Classical Quantum Gravity 10 pp 2379– (1993) · Zbl 0802.53045
[16] L. B. Szabados, Classical Quantum Gravity 11 pp 1847– (1994) · Zbl 0820.53069
[17] S. A. Hayward, Phys. Rev. D 49 pp 831– (1994)
[18] J. Katz, Phys. Rev. D 55 pp 5957– (1997)
[19] J. Jezierski, Gen. Relativ. Gravit. 22 pp 1283– (1990) · Zbl 0716.58038
[20] J. Kijowski, Gen. Relativ. Gravit. 29 pp 307– (1996) · Zbl 0873.53070
[21] D. Christodoulou, in: Mathematics and General Relativity, (1988)
[22] G. Bergqvist, Classical Quantum Gravity 9 pp 1917– (1992) · Zbl 0762.53047
[23] C. M. Chen, Phys. Lett. A 203 pp 5– (1995) · Zbl 1020.83545
[24] C. M. Chen, Classical Quantum Gravity 16 pp 1279– (1999) · Zbl 0937.83012
[25] T. Regge, Ann. Phys. (N.Y.) 88 pp 286– (1974) · Zbl 0328.70016
[26] J. Kijowski, in: A Symplectic Framework for Field Theories, (1979) · Zbl 0439.58002
[27] J. M. Nester, in: Asymptotic Behavior of Mass and Space-Time Geometry, (1984)
[28] J. M. Nester, Mod. Phys. Lett. A 6 pp 2655– (1991) · Zbl 1020.83508
[29] R. P. Wallner, Acta Phys. Austriaca 52 pp 121– (1980)
[30] J. N. Goldberg, Phys. Rev. 111 pp 315– (1958) · Zbl 0089.20903
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