Publication: On the b-completion of certain quotient-spaces
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1988-05
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Kluwer Academic
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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) 263-2681 and Johnson [The bundle boundary in some
special cases, J. Math. Phys. 18 (5) (1977) 898-9021 on the closed Friedmann model.
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[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.
[3] C.T.J. Dodson, Spacetime edge geometry, Int. J. Theoret. Phys. 17 (6) (1978) 389-504.
[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.