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On the differential topology of space-time†

Published online by Cambridge University Press:  24 October 2008

J. Wolfgang Smith
J. Wolfgang Smith
Affiliation:
Department of Mathematics, Oregon State University
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Extract

It has often been assumed in cosmology theory(1) that there exists an average density of matter in space which is everywhere greater than zero. Under this assumption the space-time M will be foliated by curves each of which represents the life history of a particle. In keeping with the postulates of general relativity theory we shall refer to these curves as geodesics. Letting X denote the space of particles one obtains a projection f: M → X which assigns to every P ∈ M the particle found at P. Conversely, given the projection f:M → X, one can recover the geodesics: they are precisely the fibres f−1(x), x∈X.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 2 , March 1971 , pp. 295 - 296
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Einstein, A.The meaning of relativity, pp. 109–114 (Princeton University Press, 1955).Google Scholar
(2)Lichnerowicz, A.Théories relativistes de la gravitation et de l'electromagnétisme, p. 109 (Paris; Masson et Cie, 1955).Google Scholar
(3)Smith, J. W.An exact sequence for submersions. Bull. Amer. Math. Soc. 74 (1968), 233–236.CrossRefGoogle Scholar
(4)Sternrod, N.The topology of fibre bundles (Princeton University Press, 1951).CrossRefGoogle Scholar
(5)Wheeler, J. A.Geometrodynamics (London; Academic Press, 1962).Google Scholar