Abstract
In many cases the spatially homogeneous cosmological models of General Relativity begin or end at a “big bang” where the density and temperature of the matter in the universe diverge. However in certain cases the spatially homogeneous development of these universes terminates at a singularity where all physical quantities are well—behaved (a “whimper”) and an associated Cauchy horizon. We examine the existence and nature of these singularities, and the possible fate of matter which crosses the Cauchy horizon in such a universe. The nature of both kinds of singularity is illustrated by simple models based on two-dimensional Minkowski space-time; and the possibility of other types of singularity occuring is considered.
This is a preview of subscription content, access via your institution.
References
Robertson, H. P.: Rev. Mod. Phys.5, 62 (1933). Weinberg, S.: Gravitation and Cosmology, New York: Wiley 1972. Peebles, P. J. E.: Physical Cosmology, Princeton 1972
Ellis, G. F. R.: Relativistic Cosmology. In: Sachs, R. K. (Ed.): General relativity and cosmology, XLVII Enrico Fermi Summer School Proceedings, 104. New York: Academic Press 1971. Ellis, G. F. R.: Relativistic cosmology, In: Schatzmann, E. (Ed.): Proceedings of the 1971 Cargese Summer School. New York: Gordon and Breach 1973
Hawking, S. W., Penrose, R.: Proc. Roy. Soc. (London) A314, 529 (1970)
Hawking, S. W., Ellis, G. F. R.: The large scale structure of space-time, Cambridge 1973
Lifschitz, E. M., Khalatnikov, I. M.: Advan. Phys. (Phil. Mag. Suppl.)12, 185 (1963)
Belinskii, V. A., Khalatnikov, I. M., Lifshitz, E. M.: Advan. Phys. (Phil. Mag. Suppl.)19, 523 (1970)
Schucking, E.: Relativistic cosmology. In: Witten, L. (Ed.): Gravitation, 438. New York: Wiley 1962. Kantowski, R., Sachs, R. K.: J. Math. Phys.7, 443 (1966)
Shepley, L. C.: Proc. Nat. Acad. Sci.52, 1403 (1964)
Hawking, S. W., Ellis, G. F. R.: Phys. Lett.17, 246 (1965)
Ellis, G. F. R., MacCallum, M. A. H.: Commun. math. Phys.12, 108 (1969); MacCallum, M. A. H.: Commun. math. Phys.20, 57 (1971)
King, A. R., Ellis, G. F. R.: Commun. math. Phys.31, 209 (1973)
Matzner, R. A., Shepley, L. C., Warren, J. B.: Ann. Phys. (New York)57, 401 (1970)
Matzner, R. A.: J. Math. Phys.11, 2432 (1970)
Shepley, L. C.: Phys. Lett.28A, 695 (1969)
Schmidt, B. G.: J. Gen. Rel. Grav.1, 269 (1971); Commun. math. Phys.29, 49 (1972)
Schmidt, B. G., Ellis, G. F. R.: Unpublished
Clarke, C. J. S.: Commun. math. Phys.32, 205 (1973)
Geroch, R. P.: J. Math. Phys.8, 782 (1967)
Farnsworth, D. L.: J. Math. Phys.8, 2315 (1967)
Ellis, G. F. R.: J. Math. Phys.8, 1171 (1967)
Schmidt, B. G.: Commun. math. Phys.15, 329 (1969)
Boyer, R. H.: Proc. Roy. Soc. (Lond.) A311, 245 (1969)
Carter, B.: J. Math. Phys.10, 70 (1969)
Carter, B.: Domains of stationary communication. Preprint. Cambridge (1972)
MacCallum, M. A. H., Taub, A. H.: Commun. math. Phys.25, 173 (1972)
Treciokas, R., Ellis, G. F. R.: Commun. math. Phys.23, 1 (1971)
Eardley, D., Liang, E., Sachs, R. K.: J. Math. Phys.13, 99 (1972)
MacCallum, M. A. H., Ellis, G. F. R.: Commun. math. Phys.19, 31 (1970)
Hawking, S. W.: Mon. Not. Roy. Ast. Soc.142, 129 (1969); Collins, C. B., Hawking, S. W.: Mon. Not. Roy. Ast. Soc.162, 307 (1973)
Misner, C. W.: Minisuperspace. In: Magic without magic. Wheeler Festschrift (1973).
Ryan, M.: Hamiltonian cosmology. Lecture Notes in Physics13, Berlin-Heidelberg-New York: Springer 1972
Stormer, O.: Doctoral thesis, Hamburg University (1971) Osinovsky, M. E.: Preprint, Kiev (1973)
Author information
Authors and Affiliations
Additional information
Communicated by J. Ehlers
Rights and permissions
About this article
Cite this article
Ellis, G.F.R., King, A.R. Was the big bang a whimper?. Commun.Math. Phys. 38, 119–156 (1974). https://doi.org/10.1007/BF01651508
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01651508
Keywords
- Neural Network
- Statistical Physic
- General Relativity
- Complex System
- Simple Model