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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
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