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A “Cubical” Universe

Published online by Cambridge University Press:  20 January 2009

W. H. McCrea
W. H. McCrea
Affiliation:
Edinburgh University.
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Einstein has studied a universe in which the time coordinate t is uncurved and the spatial section is the surface of a sphere

in four dimensions. Some interest attaches to the case where this surface is replaced by

where n is a positive integer.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 2 , Issue 3 , January 1931 , pp. 158 - 163
Copyright
Copyright © Edinburgh Mathematical Society 1931

References

page 158 note 1 Eddington, , Mathematical Theory of Relativity (1924), §67.Google Scholar

page 158 note 2 Such approximations have been discussed in a recent communication to the Society by Professor J. E. A. Steggall.Google Scholar

page 159 note 1 Eddington, , op. cit., §65.Google Scholar

page 159 note 2 When n is large our space is almost “flat” except at the corners, so that it cannot take account of λ which would require a non-zero curvature everywhere. See § 5 below.Google Scholar

page 160 note 1 Since, for example, the difference between and is appreciable only when this term is small compared with or and vice versa. The error is of order .Google Scholar

page 162 note 1 These results are for a “spherical” space in which the curvature is due entirely to the matter present, Einstein's cosmical constant being neglected.Google Scholar