Abstract
The problems of the tolal energy and quasilocalenergy density or an isolated spherically symmetric static system in general relativity (GR) are considered with examples of some exact suintions. The field formulation of GR dereloped earlier hy L. P. Grishchuk. el al. (1984). in ihe framework of which all the dynamical fields, including the gravitation field, are considered in a fixed background spacetime is used intensively. The exact Schwarzschild and Reissner Nordstrom solutions are investigated in detail, and the results are compared with those in the recent work by J. D. Brown and J. W. York. Jr. (1993) as well as discussed with respect to the principle of nonlocalization of the gravitational energy in GR. Those examples are illustrative and simple because the background is selected as Minkowski spacetime and, in fact, the field configurations are studied in the framework of special relativity. It is shown that some problems of the Schwarzschild solution which are difficult to resolve in the standard geometrical framework of GR are resolved in the framework of the field formulation.
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References
C. W. Misner, K. S. Thorne, and J. A. Wheeler.Graritation (Freeman, San Francisco. 1973).
J. Katz and A. Ori.Class. Quantum Gravit. 7, 787 (1990).
J. D. Brown and J. W. York, Jr.,Phys. Rev. D 47. 1407 (1993).
J. W. Maluf.J. Math. Phys. 36, 4242 (1995).
D. Kennefick and N. O’Murchadha.Class. Quantum Gnravit. 12, 149 (1995).
K. Rosquist,Class. Quantum Gravit. 12, 1305 (1995).
J. V. Narlikr.Am. J. Phys. 62, 903 (1994).
K. K. Nandi and A. Islam.Am. J. Phys. 63, 251 (1995).
J. L. Synge,Relativity: The General Theory (North-Holland, Amsterdam, 1960).
L. P. Girishchuk. A. N. Petrov. and A. D. Popova.Commun. Math. Phys. 94. 379 (1984).
A. D. Popova and A. N. Petrov.Im. J. Mod. Phys. A 3, 2651 (1988).
A. N. Petrov.Class. Quantum Gravit. 10, 2663 (1993).
J. V. Narlikar. “Some conceptual problems in general relativity and cosmology.” in:A Random Walk in Relativity and Cosmology. N. Dadhich, J. Krishna Rao, J. V. Narlikar. and C. V. Vishevara. eds. (Wiley Eastern, New Delhi. 1985). pp. 171 183.
N. Dadhich, “How empty must empty space be” Report (The Third International Conference on Gravitation and Cosmology. Pune. India. December 13 19. 1995).
L. D. Landau and E. M. Lifshitz.The Classical Theory of Fields (Pergamon. Oxford. 1975).
H. Bondi.Proc. Roy. Soc. London A 281, 39 (1964).
R. Schoen and S.-T. Yau.Common. Math. Phys. 65. 45 (1979):79, 231 (1981).
E. Witten,Commun. Math. Phys. 80, 381 (1981).
A. N. Petrov.Int. J. Mod. Phys. D 4, 451 (1995).
H. Balasin and H. Nachbagauer.Class. Quantum Gravit. 10, 2271 (1993).
T. Regge and C. Teitelboim.Ann. Phys. (N.Y.) 88. 286 (1974).
A. N. Petrov,Astronom. Astrophys. Trans. 1, 195 (1992).
P. S. Florides.Gen. Relat. Gravit. 26, 1145 (1994).
N. O’Murchadha.J. Math. Phys. 27, 2111 (1986).
A. N. Petrov. “On the weakest falloff conditions in the metric for an isolated system”. Preprint: IUCAA-32 95 (1995).
J. Katz.Class. Quantum Gravit. 2, 423 (1985).
J. W. Maluf,J. Math. Phys. 35, 335 (1994).
J. Jezierski and J. Kijowski.Gen. Relat. Gravit. 22, 1283 (1990): J. M. Nester,Class. Quantum Gravit. 8, LI9 (1991): G. Bergqvist and M. Ludvigsen,Class. Quantum Gravit. 8, 697 (1991): A. J. Dugan and L. J. Mason.Phys. Rev. Lett. 67, 2119 (1991) S. Lau.Class. Quantum Gravit. 10, 2397 (1993): T. Shiromizu and M. Sugai,Class. Quantum Gravit. 11, L103 (1994).
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Petrov, A.N., Narlikar, J.V. The energy distribution for a spherically symmetric isolated system in general relativity. Found Phys 26, 1201–1229 (1996). https://doi.org/10.1007/BF02275626
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DOI: https://doi.org/10.1007/BF02275626