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The b-completion of the Friedmann space

Amores Lázaro, Ángel Miguel and Gutiérrez, M (1999) The b-completion of the Friedmann space. Journal of geometry and physics, 29 (01-feb). pp. 177-197. ISSN 0393-0440

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Abstract

We study the b-completion of the three Friedmann models of the Universe, having as models for 3-space the sphere, the Euclidean space or the hyperbolic space. We show that in the first case there is just one singularity, having the full completion as only neighborhood. In the other two cases there is one essential singularity, which is the limit of all past causal geodesics; again, it has a single neighborhood. This extends results by Bosshard [On the b-boundary of the closed Friendmann Model, Commun. Math. Phys. 46 (1976) 263-268] and Johnson [The bundle boundary in some special cases, J. Math. Phys. 18 (5) (1977) 898-902] on the closed Friedmann model. (C) 1999 Elsevier Science B.V. All rights reserved.

Item Type:Article
Uncontrolled Keywords:Singularities; B-completion; Friedmann space, Mathematics, Applied; Physics, Mathematical
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14714
References:

[l] B. Bosshard, On the b-boundary of the closed Friedmann model, Commun. Math. Phys. 46 (1976)

263-268.

[2] D. Canarutto, An introduction to the geometry of singularities in general relatively, Riv. Nuovo Cimento

11 (3) (1988) l-60.

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[4] SW. Hawking, G.F.R. Ellis, The Large-Scale Structure of Spacetime, University Press, Cambridge, 1973.

[5] R.A. Johnson, The bundle boundary in some special cases, .I. Math. Phys. 18 (5) (1977) 898-902.

[6] M.A. Naimark, Les representations lineaires du groupe de Lorentz, Dunod, Paris, 1962.

[7] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York,

1982.

[S] B.G. Schmidt, A new definition of singular points in general relativity, Gen. Rel. Grav. 1 (3) (1971)

269-280.

Deposited On:17 Apr 2012 10:02
Last Modified:06 Feb 2014 10:07

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