Abstract
Linearized solution of Datta in a non-symmetric and isentropic motion of a perfect fluid is studied by dealing with a Cauchy problem in co-moving coordinates in the framework of general relativity. The problem of singularities is discussed from the standpoint of a local observer both for rotating and non-rotating fluids. It is shown that, whatever the distribution of matter, a singularity which occurred in the past in both the rotating and non-rotating parts of the universe must occur again later after some finite proper time, if the universe is closed. A modification is incorporated in Penrose’s theorem by explicitly exhibiting that the universe defined by Penrose can possess a Cauchy hypersurface.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bera K and Datta B K 1974Physica 72 616
Bera K and Datta B K 1975 GRG6 129
Brans C and Dicke R H 1961Phys. Rev. 124 925
Chiu H J 1965 Presented at the Buenos Aires Meeting of COSPAR, summarizing earlier work preprint
Datta B K 1975–76 Proc. Int. Symp. on Relativity and Unified Field Theory
Datta B K 1977Prog. Theor. Phys. (in press)
Ellis G F R 1971General Relativity and Cosmology ed. R K Sachs (New York, London: Academic Press)
Geroch R P 1966Phys. Rev. Lett. 17 446
Gödel K 1949Rev. Mod. Phys. 21 447
Gratton L and Szamosi 1964Nuovo Cimento 33 1056
Gratton L 1966High-Energy Astrophysics ed. L Gratton (New York, London: Academic Press) pp. 1–9
Hawking S W 1966Proc. R. Soc. (London) A295 490
Hawking S W 1967Proc. R. Soc. (London) A300 187
Hawking S W and Ellis G F R 1968Astrophys. J. 152 25
Hawking S W and Penrose R 1970Proc. R. Soc. (London) 314 529
Kopczyński W 1972Phys. Lett. A39 219
Kopczyński W 1973Phys. Lett. A43 63
Landau L D 1932Phys. Z. Sowjetunion 1 285
Landau L D and Lifshitz E M 1962The Classical Theory of Fields 2nd ed. (Oxford: Pergamon Press) p. 271
Lifshitz E M and Khalatnikov I M 1963Usp. Fiz. Nauk 80 391 (English translation:Sov. Phys, Uspekhi 6 495 (1963))
Marx G and Németh 1965 preprint
Oppenheimer J R and Snyder H 1939Phys. Rev. 56 455
Oppenheimer J R and Volkoff G M 1939Phys. Rev. 55 374
Pachner J 1970 GRG1 281
Penrose R 1965Phys. Rev. Lett. 14 57
Raychaudhuri A K 1955Phys. Rev. 98 1123
Tafel J 1973Phys. Lett. A45 341
Taub A H 1956Phys. Rev. 103 454
Tauber G E and Weinberg J W 1961Phys. Rev. 122 1342
Thorne K S 1966High-Energy Astrophysics ed. L Gratton (New York, London: Academic Press) pp. 166–220
Trautman A 1972a Warsaw preprint IFT/13
Trautman A 1972b GRG3 167
Trautman A 1973Nature 242 7
Wolfe A M 1970Astrophys. J. 159 161
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Datta, B.K. Initial-value problems and singularities in general relativity. Pramana - J Phys 9, 229–238 (1977). https://doi.org/10.1007/BF02846202
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02846202