Abstract
Consideration is given to the possibility that the whole matter of the Universe possesses a dilatational degree of freedom. This effect is assumed to be a cause requiring the use of non-Euclidean geometry in the framework of general relativity and cosmology. In this case, however, we assert that non-Euclideanism does not reflect an intrinsic property of the space. Accordingly we propose the concept of a finite and unbounded universe whose extent has nothing to do with the shape of the hypersphere.
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References
Adler, R., Bazin, M., and Schiffer, M.: 1975,Introduction to General Relativity, McGraw-Hill Kogakusha Ltd., New York.
Čadež, V.: 1985, private communications.
d'Abro, A.: 1950,The Evolution of Scientific Thought from Newton to Einstein, Dover Publ. Inc., New York.
Eddington, A. S.: 1947,The Nature of the Physical World, J. M. Dent and Sons Ltd., London.
Einstein, A.: 1955,The Meaning of Relativity, Princeton Univ. Press.
McVittie, G. C.: 1965,General Relativity and Cosmology, Univ. of Illinois Press, Urbana.
Pavšić, M.: 1975,Int. J. Theor. Phys. 14, 299.
Selak, S.: 1984,Astrophys. Space Sci. 107, 357.
Selak, S.: 1985,Astrophys. Space Sci. 109, 123.
Stojkov, P.: 1985, private communication.
Weyl, H.: 1918,Gravitation und Elektrizität, Sitzber. Preuss. Akad. Wiss., Berlin, pp. 465–480.
Weyl, H.: 1922,Space, Time, Matter, Dover Publ. Inc., New York.
Weyl, H.: 1949,Philosophy of Mathematics and Natural Science, Princeton.
Whittaker, E. T.: 1958,From Euclid to Eddington, Dover Publ. Inc., New York.
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Selak, S. Non-Euclideanism in general relativity and cosmology. Astrophys Space Sci 127, 117–131 (1986). https://doi.org/10.1007/BF00637767
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DOI: https://doi.org/10.1007/BF00637767