On the construction of effective metrics in a relational model of space-time

S.V. Bolokhov1, A.N. Klenitsky2


Within the scope of the relational model of spacetime developed by Yu.S. Vladimirov, we consider a toy model of test particle motion in an effective gravitational field described in terms of the modified Fokker-Feynman-Wheeler direct particle interaction formalism. It is shown that an agreement with the classical GR result (perihelion shift of a planetary orbit) can be obtained in the minimal nonlinear approximation in G under some simple assumptions.


  1. Yu. S. Vladimirov, Relational Theory of Space-Time and Interactions. Parts 1, 2 (MSU Publishing House, Moscow, 1996, in Russian).
  2. Yu. S. Vladimirov, Foundations of Physics (Moscow, BINOM, 2008, in Russian).
  3. Yu. S. Vladimirov, Binary Geometrophysics: Space-Time, Gravitation, Grav. Cosmol. 1, 184 (1995).
  4. S. V. Bolokhov, On the Description of Lorentz Reference Frames in a Relational Model of Space-Time, Grav. Cosmol. 15, 28 (2009).
  5. S. V. Bolokhov and Yu. S. Vladimirov, An Algebraic Approach to the Description of Electroweak and Strong Interactions, Grav. Cosmol. 9, 113 (2003).
  6. A. D. Fokker, Ein invarianter Variationssatz fur die Bewegung mehrerer electrischer Massenteilchen, Z.Phys.Bd. 58, 386 (1929).
  7. J. A. Wheeler and R. P. Feynman, Interaction with the Absorber as the Mechanism of Radiation, Rev. Mod. Phys. 17, 157 (1945).
  8. Yu. S. Vladimirov and A. Yu. Turygin, Theory of Direct Particle Interaction (Moscow, Energoatomizdat, 1986, in Russian).
  9. A. Yu. Turygin, Fokker's Type Action at a Distance Theory of Gravitation, Gen. Rel. Grav. 18, 333 (1986).
  10. Yu. S. Vladimirov, Gravitational Interaction in the Relational Approach, Grav. Cosmol. 14, 41 (2008).
  11. Ya. I. Granovsky and A. A. Pantiushin, On the Relativistic Gravitation Theory, Izvestija AN Kaz. SSR, Phys.-Math. Series 2, 65 (1965) (in Russian).
  12. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman and Company, San Francisco, 1973), Vol. 3.
  13. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Butterworth-Heinemann, 1975).
For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page