Astrophysics and Space Science

, Volume 121, Issue 1, pp 161–191 | Cite as

cD galaxies of apparent supergiant sizes due to the curvature of space

  • Jaroslav Souček


By combining two two-dimensional subspaces, closed into themselves due to curvature, it is possible to create a model of three-dimensional space of the same properties. If the Universe is a space of this type, its effect is that of a monstrous lens. Close objects are observed to diminish according to the normal law of perspective; however, the remote galaxies are seen to be very highly magnified.

The apparent angular size2θ of a galaxy is more than the size1θ in flat space according to relation:2θ =1θχ cosec χ, where χ is the angular distance from the observer to the galaxy. The diameter2d of a galaxy in curved space must be in the same relation to a diameter1d with no curvature of space:2d=1dχ cosec χ. The apparent angular size2θ and diameter2d are distorted shapes in consequence of an optical illusion caused by the spatial curvature.

It is necessary to distribute the multitude of galaxies into two parts in accordance with their location on the close or reverse hemihypersphere of the Universe. The minimum of apparent angular size2θ of a galaxy of diameter1d is at the equatorial zone.

The most likely candidates for location in the reverse hemi-hypersphere are cD's of apparent supergiant sizes due, probably, to the curvature of space. The existence of supergiant sizes of galaxies is the second indirect proof, besides superluminal velocities, that the Universe is closed into itself through curvature. The third indirect evidence, i.e., inductive confirmation of the same fact, is the superposition of galaxies which need not inevitably be a new alternative to the present theories of collisions, cannibalism, merger, etc.

The fourth indirect proof of the positive curvature of the Universe is the occurrence of background radiation, because that must vanish in hyperbolic space irrespective of its origin. The gravitational lens effect acquires another theoretical form, as usual, in the case of remote galaxies, because it is impossible to distinguish between gravitator and lensing image.


Hyperbolic Space Positive Curvature Angular Distance Distort Shape Flat Space 
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© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Jaroslav Souček
    • 1
  1. 1.Astronomical SocietyCzechoslovak Academy of SciencesPragueCzechoslovakia

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