By Abraham Zelmanov, D. Rabounski, S. Crothers, L. Borissova

ISBN-10: 1599730111

ISBN-13: 9781599730110

This e-book used to be written in 1944 by means of Abraham Zelmanov, a favorite scientist operating ordinarily relativity and cosmology. Herein he constructs the speculation of actual observable amounts regularly Relativity (Chronometric Invariants), and applies it to figure out all attainable cosmological types in the framework of Einstein conception eventualities of evolution which may be theoretically feasible for a very inhomogeneous and anisotropic Universe.

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311). Finally, it was generalized for the case of Λ = 0 (see [2], p. 319). In the last case, Newton’s law of gravitation must be generalized by introducing an additional force, producing an additional relative acceleration of two interacting particles (the acceleration equals the product of 13 Λc2 and the distance between the particles). 5) r and the integral of energy 3 ε r˙ 2 − 6 2 = 8πγρ + Λc2 . 4) in the case of p = 0. It is evident that the analogy we have considered facilitates determination of a link between the dynamics and the geometry of the relativistic homogeneous universe — the link between the evolution scenario of the models and the space curvature.

3)  Λ = 0, k = −1 , M1      Λ < 0, k = −1 , O1 3 To draw conclusions which would be more likely than the above, and to make quantitative tests of the relativistic cosmological equations, more detailed observational data are needed on one hand and, on the other hand, some additional theoretical correlations between the observable values we use in the cosmological models. More detailed statistical data had been collected by Hubble [37]. Those data concern: (a) the average spectral type of galaxies; λ in the spectra of λ the galaxies; their photographic stellar magnitudes go up to m =17; (c) the number of the galaxies N (m), absolute stellar magnitudes of which go up to m = 21.

We are now going to consider the general case of the equations of the law of gravitation and of the law of energy in the accompanying coordinates. The quantities ρ and p, characterizing the state of matter, are contained in components of Tμν , which consist of the equation of gravitation and the equation of energy. The quantity D, describing the evolution (i. e. deformations) of the substance and of its ac∂gik companying space, must evidently be linked to the quantities , ∂x0 which are contained in the equation of gravitation and the equation of energy as well.

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Chronometric invariants by Abraham Zelmanov, D. Rabounski, S. Crothers, L. Borissova

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