Skip to main content
SpringerLink
Log in

Non-Archimedean Algebra: Applications to Cosmology and Gravitation

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

Application of recently developed non-Archimedean algebra to a flat and finite universe of total mass M 0 and radius R 0 is described. In this universe, mass m of a body and distance R between two points are bounded from above, i.e., 0≤m≤M 0, 0≤R≤R 0. The universe is characterized by an event horizon at R 0 (there is nothing beyond it, not even space). The radial distance metric is compressed toward horizon, which is shown to cause the phenomenon of red shift. The corresponding modified Minkowski's metric and Lorentz transforms are obtained. Applications to Newtonian gravity shows a weakening at large scales (R→R 0) and a regular behavior as R→0.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. K. Avinash, Specul. Sci. Technol. 9, 291 (1986).

    Google Scholar 

  2. V. L. Rvachev, Sov. Phys. Dokl. 36(2), 130 (1991).

    Google Scholar 

  3. P. K. Rashevskii, Usp. Mat. Nauk. 28, 243 (1973).

    Google Scholar 

  4. V. L. Rvachev and A. V. Dabagyan, Sov. Phys. Dokl. 37(10), 497 (1992).

    Google Scholar 

  5. V. L. Rvachev, Sov. Phys. Dokl. 36(12), 803 (1991).

    Google Scholar 

  6. V. F. Kravchenko, V. L. Rvachev, A. N. Shevchenko, and T. I. Sheiko, Radiotekhn. Elektron. 7, 1076_1094 (1995).

    Google Scholar 

  7. G. Bothun, Modern Cosmological Observations and Problems (Taylor 6 Francis, London, 1998).

    Google Scholar 

  8. W. Rindler, Notices Roy. Astron. Soc. 116, 662 (1956).

    Google Scholar 

  9. V. Sabbata and M. Gasperini, Introduction to Gravitation (World Scientific, Singapore, 1985).

    Google Scholar 

  10. E. Harrison, Cosmology__The Science of the Universe (Cambridge University Press, Cambridge, 1981).

    Google Scholar 

  11. H. C. Arp and T. Van Flandern, Phys. Lett. A 164, 263 (1992).

    Google Scholar 

  12. I. E. Segal, J. F. Nicoll, P. Wu, and Z. Zhou, Ap. J. 411, 465 (1993).

    Google Scholar 

  13. V. S. Troitskii, Astrophys. Space Sci. 201, 203 (1993).

    Google Scholar 

  14. E. Milne, Q. J. Math. 5, 64 (1934).

    Google Scholar 

  15. A. Guth, Phys. Rev. D 23, 347 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International Centre for Theoretical Physics, Trieste, Italy

    K. Avinash

  2. Institute for Problems in Machinery, Ukrainian National Academy of Sciences, Kharkov, Ukraine

    V. L. Rvachev

Authors
  1. K. Avinash
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. L. Rvachev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avinash, K., Rvachev, V.L. Non-Archimedean Algebra: Applications to Cosmology and Gravitation. Foundations of Physics 30, 139–152 (2000). https://doi.org/10.1023/A:1003647210704

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1003647210704

Keywords

Search

Navigation