Summary
The main approaches to the matching of gravitational fields ion general relativity are discussed. A special study of junction conditions in synchronous coordinates is carried out. A theorem concerning this case is formulated. It is revealed that the exterior Schwarzschild solution expressed in Gaussian coordinates is inadequate for matching with the Friedmann universe.
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References
K. Lanczós:Z. Phys.,23, 539 (1992).
K. Lanczós:Ann. Phys. (Leipzig),74, 518 (1924).
G. Darmois:Les equation de la gravitation einsteinienne, memorial des sciences mathematiques, XXV (Paris, 1927), p. 30.
J. R. Oppenheimer andH. Snyder:Phys. Rev.,56, 455 (1939).
A. Einstein andE. Straus:Rev. Mod. Phys.,18, 148 (1946).
E. Schucking:Z. Phys.,137, 595 (1954).
C. Gilbert:Mon. Not. R. Astron. Soc.,116, 678 (1956).
F. Hoyle andJ. V. Narlikar:Proc. R. Soc. Lond. Ser. A,278, 465 (1964).
H. Nariai:Prog. Theor. Phys.,34, 173 (1965).
S. O’Brien andJ. L. Synge:Commun. Dublin Inst. Adv. Stud., Ser. A, no. 9, 1 (1952).
W. Just:Z. Astrophys.,49, 19 (1960).
M. M. Kumar andB. P. Singh:Prog. Theor. Phys.,52, 1068 (1974).
A. J. Galloway:Prog. Theor. Phys.,116, 678 (1981).
W. B. Bonner andP. A. Vickers:Gen. Relativ. Gravit.,13, 29 (1981).
A. Lichnerowicz:Theories relatistes de la gravitation et de l’electromagnetisme (Masson, Paris, 1955), p. 61.
W. Israel:Proc. R. Soc. London, Ser. A,248, 404 (1958).
E. H. Robson:Ann. Inst. Henri Poincaré,16, 41 (1972).
R. V. Lindquist andJ. A. Wheeler:Rev. Mod. Phys.,29, 432 (1957).
W. Israel:Nuovo Cimento,44, 1 (1965).
J. L. Synge:Relativity: The General Theory (North-Holland, Amsterdam, 1960).
K. Leibovic:Nuovo Cimento B,60, 254 (1969).
G. C. McVittie:Astrophys. J.,140, 401 (1964).
G. C. McVittie andR. Stabbel:Ann. Inst. Henri Poincaré, Sect. A,7, 103 (1967).
Y. Nariai:Prog. Theor. Phys.,37, 761 (1967).
P. A. Vickers:Ann. Inst. Henri Poincaré,18, 137 (1973).
W. B. Bonner andM. C. Faulkes:Mon. Not. R. Soc.,137, 239 (1967).
W. B. Bonner:Commun. Math. Phys.,51, 191 (1967).
W. J. Cocke:J. Math. Phys.,7, 1171 (1966).
N. F. Dandach:Nuovo Cimento B,103, 603 (1989).
C. W. Misner, K. S. Thorne andj. A. Wheele:Gravitation (San Francisco, 1973).
N. V. Mitskievic andN. F. Dandach:On the matching conditions, Abstract GR-10, Padova, 1983.
N. F. Dandach Ph. D. thesis, Byelorussian University, Minsk, 1983.
N. F. Dandach andN. V. Mitskievicz:J. Phys. A,17, 2335 (1984).
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Dandach, N.F. Matching of gravitational fields in general relativity: Junction conditions in synchronous and in Gaussian coordinates. Nuov Cim B 107, 1267–1277 (1992). https://doi.org/10.1007/BF02726092
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DOI: https://doi.org/10.1007/BF02726092