International Journal of Theoretical Physics

, Volume 52, Issue 11, pp 4074–4082 | Cite as

Multivariance as Immanent Property of the Space-Time Geometry

Article

Abstract

It shown that the space-time geometry is multivariant, and one cannot describe it completely, using formalism of the linear space. Tachyons and tachyon gas cannot be described in terms of the linear space formalism. To describe correctly the space-time geometry, one needs to use the metric approach and description in terms of the world function. In the framework of metric approach to geometry one can explain freely the dark matter nature.

Keywords

Multivariant geometry Metric approach Restriction on coordinates Tachyon gas Dark matter Galiley phenomenon 

References

  1. 1.
    Rylov, Yu.A.: Geometry without topology as a new conception of geometry. Int. J. Math. Math. Sci. 30(12), 733–760 (2002). See also arXiv:math.MG/0103002 MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Synge, J.L.: A characteristic function in Riemannian space and its applications to the solution of geodesic triangles. Proc. Lond. Math. Soc. 32, 241 (1932) MathSciNetGoogle Scholar
  3. 3.
    Ruse, H.S.: Some teorem in tensor calculus. Proc. Lond. Math. Soc. 31, 225 (1930) MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Synge, J.L.: Relativity: the general theory. North-Holland, Amsterdam Google Scholar
  5. 5.
    Rylov, Yu.A.: Different conceptions of Euclidean geometry and their application to the space-time geometry. arXiv:0709.2755v4
  6. 6.
    Sommerfeld, A.: Simplified deduction of the field and the forces of an electron moving in any given way. In: Knkl. Acad. Wetensch, vol. 7, pp. 345–367 (1904) Google Scholar
  7. 7.
    Bilaniuk, O.-M.P., Deshpande, V.K., Sudarshan, E.C.G.: ‘Meta’ relativity. Am. J. Phys. 30(10), 718 (1962) MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Terletsky, Ya.P.: Positive, negative and imaginary rest masses. J. Phys. Radium 23(11), 910–920 (1963) CrossRefGoogle Scholar
  9. 9.
    Feinberg, G.: Possibility of faster-than-light particles. Phys. Rev. 159(5), 1089–1105 (1967) ADSCrossRefGoogle Scholar
  10. 10.
    Feinberg, G.: Phys. Rev. D 17, 1651 (1978) ADSCrossRefGoogle Scholar
  11. 11.
    Rylov, Yu.A.: Dynamic equations for tachyon gas. IJTP (now this paper can be found on my site http://rsfq1.physics.sunysb.edu/~rylov/detg1e.pdf). doi: 10.1007-013-1674-4
  12. 12.
    Merritt, D., et al.: Empirical models for dark matter halos. I. Nonparametric construction of density profiles and comparison with parametric models. Astron. J. 132(6), 2685–2700 (2006) ADSCrossRefGoogle Scholar
  13. 13.
    Rylov, Yu.A.: Discrete space-time geometry and skeleton conception of particle dynamics. Int. J. Theor. Phys. 51(6), 1847–1865 (2012). See also arXiv:1110.3399v1 MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Rylov, Yu.A.: Non-Riemannian model of the space-time responsible for quantum effects. J. Math. Phys. 32(8), 2092–2098 (1991) MathSciNetADSCrossRefMATHGoogle Scholar
  15. 15.
    Rylov, Yu.A.: Is the Dirac particle composite? arXiv:physics/0410045
  16. 16.
    Rylov, Yu.A.: Is the Dirac particle completely relativistic? arXiv:physics/0412032
  17. 17.
    Rylov, Yu.A.: Geometrical dynamics: spin as a result of rotation with superluminal speed. arXiv:0801.1913
  18. 18.
    Rylov, Yu.A.: Discriminating properties of compactification in discrete uniform isotropic space-time. arXiv:0809.2516v2
  19. 19.
    Rubakov, V.A.: On large Hadron Collider’s discovery of a new particle with Higgs boson properties. Phys. Usp. 182(10), 1017–1025 (2012) (in Russian) CrossRefGoogle Scholar
  20. 20.
    Rylov, Yu.A.: General relativity extended to non-Riemannian space-time geometry. arXiv:0910.3582v7
  21. 21.
    Rylov, Yu.A.: Induced antigravitation in the extended general relativity. Gravit. Cosmol. 18(2), 107–112 (2012) MathSciNetADSCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia

Personalised recommendations