Canonical angular supermomentum tensors in general relativity

Journal of Mathematical Physics

Volumn 40, Issue 8, 1999, Pages 4035-4055

  Garecki, Janusz ^a  

^a UNIVERSITY OF SZCZECIN   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033241169     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532941     Document Type: Article

References (33)

1. By "standard general relativity" we mean general relativity without any supplementary element like tetrads, second metric, or an arbitrary vector field.
2. Called canonical because it can be obtained as canonical one from a suitable Lagrangian (see Ref. 3).
3. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1975).
4. J. Garecki, in Proceedings: Einstein Centenary Symposium, Vol. II (Duhita Publishers c/o Einstein Foundation International, Nagpur, 1981).
5. J. Garecki, Int. J. Theor. Phys. 35, 2195 (1996).
6. O. B. Zaslavskii, Class. Quantum Grav. 13, L63 (1996).
7. Z. D. Christodoulou and S. T. Yau, Contemp. Math. 71, 9 (1988).
8. W. T. Shaw, Contemp. Math. 71, 15 (1988).
9. R. Penrose, Proc. R. Soc. London, Ser. A 381, 53 (1982).
10. S. A. Hayward, Phys. Rev. D 53, 1938 (1996).
11. F. A. E. Pirani, Phys. Rev. 105, 1089 (1957).
12. J. Garecki, Acta Phys. Pol. B 11, 255 (1980).
13. J. Garecki, Rep. Math. Phys. (Toruń) 40, 485 (1997).
14. J. Garecki, Rep. Math. Phys. (Toruń) 33, 57 (1993).
15. J. Garecki, "Canonical Energetic and Canonical Superenergetic Quantities for Friedman Universes," paper accepted for publication in Rep. Math. Phys. (Toruń) 43, 377 (1999).
16. J. Winicour, "Angular Momentum in General Relativity" in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980).
17. J. Goldberg, "Invariant Transformations, Conservation Laws and Energy-Momentum," in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980).
18. J. A. Schouten, Ricci Calculus (Springer-Verlag, Berlin, 1954).
19. A. Z. Petrov, New Methods In General Relativity (Nauka, Moscow, 1966) (in Russian) [English: edition of Petrov's book: Einstein Spaces (Pergamon, New York, 1969)].
20. C. Møller, Mat. Fys. Medd. K. Dan. Vidensk. Selsk. 31, 14 (1959).
21. J. L. Synge, Relativity: the General Theory (North-Holland, Amsterdam, 1960). We have used the world function σ(P;y) in the formula (1) already.
22. P. G. Bergmann and R. Thomson, Phys. Rev. 89, 401 (1953).
23. J. Garecki, Zeszyty Naukowe WSP Szczecin, 26, 25 (1978) (in Polish; summary in English).
24. Ch. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
25. J. Ehlers and W. Kundt, in Gravitation: an introduction to current research, edited by L. Witten (Wiley, New York, 1962).
26. i} mean normal coordinates. But they always form components of a geometric object (see, e.g., Ref. 18).
27. S. Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon, Oxford, 1983).
28. Calculations of these components are very simple but tedious. The analytic form of the calculated nonzero components is too complicated to be presented here.
29. 2.
30. 1). 32 See Ref. 29.
31. In special relativity the antisymmetric part of a conserved energy-momentum tensor is proportional to the ordinary divergence of the three-index tensor which describes intrinsic angular momentum density (see, e.g., Refs. 34 and 35). Here we follow this line.
32. V. Sabatta and M. Gasperini, Introduction to Gravitation (World Scientific, Singapore, 1985)
33. W. Kopczyński and A. Trautman, Space-time and Gravitation (Wiley, New York, 1992).