Gravitation and Cosmology

, Volume 23, Issue 4, pp 300–304 | Cite as

Twistor structures and boost-invariant solutions to field equations

  • Vladimir V. Kassandrov
  • Joseph A. Rizcallah
  • Nina V. Markova
Article
  • 22 Downloads

Abstract

We start with a brief overview of a non-Lagrangian approach to field theory based on a generalization of the Kerr-Penrose theorem and algebraic twistor equations. Explicit algorithms for obtaining the set of fundamental (Maxwell, SL(2,ℂ)-Yang-Mills, spinor Weyl and curvature) fields associated with every solution of the basic system of algebraic equations are presented. The notion of a boost-invariant solution is introduced, and the unique axially-symmetric and boost-invariant solution which can be generated by twistor functions is obtained, together with the associated fields. It is found that this solution possesses a wide variety of point-, string- and membrane-like singularities exhibiting nontrivial dynamics and transmutations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Penrose and W. Rindler, Spinors and Space-Time, vol. 1, 2 (Cambridge University Press, Cambridge, 1984)Google Scholar
  2. 2.
    G. C. Debney, R. P. Kerr, and A. Schild, J. Math. Phys. 10, 1842 (1969).ADSCrossRefGoogle Scholar
  3. 3.
    V. V. Kassandrov, Algebraic Structure of Space-Time and Algebrodynamics (Peoples’ Friendship University Press, Moscow, 1992) (in Russian).MATHGoogle Scholar
  4. 4.
    V. V. Kassandrov, Grav. Cosmol. 3, 216 (1995); grqc/0007027.ADSGoogle Scholar
  5. 5.
    V. V. Kassandrov and J. A. Rizcallah, Grav. Cosmol. 22, 230 (2016); arXiv: 1510.01228.ADSCrossRefGoogle Scholar
  6. 6.
    V. V. Kassandrov and J. A. Rizcallah, Int. J. Geom. Methods Mod. Phys. 14, 1750031 (2017); arXiv: 1612.06718.MathSciNetCrossRefGoogle Scholar
  7. 7.
    V. V. Kassandrov, in Has the Last Word Been Said on Classical Electrodynamics?, Ed. by A. Chubykalo et al. (Rinton Press, 2004), pp. 42–67; arXiv: physics/0308045.Google Scholar
  8. 8.
    Joseph A. Rizcallah, Geometrization of Electromagnetism on the Basis of Spaces with Weyl-Cartan Connections, PhD thesis (RUDN University, Moscow, 1999) [in Russian].Google Scholar
  9. 9.
    V. V. Kassandrov and A. V. Tretyakova, Bull. Peoples’ Friend. Univ: Math., Inform., Phys., No. 3, 89 (2009).Google Scholar
  10. 10.
    F. Rorlich, Classical Charged Particles (World Scientific, 2007), p. 118.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • Vladimir V. Kassandrov
    • 1
  • Joseph A. Rizcallah
    • 2
  • Nina V. Markova
    • 3
  1. 1.Institute of Gravitation and CosmologyPeoples’ Friendship University of RussiaMoscowRussia
  2. 2.School of EducationLebanese UniversityBeirutLebanon
  3. 3.Department of Applied MathematicsPeoples’ Friendship University of RussiaMoscowRussia

Personalised recommendations