Skip to main content
SpringerLink
Log in

On Relativistic Generalization of Gravitational Force

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

In relativistic theories, the assumption of proper mass constancy generally holds. We study gravitational relativistic mechanics of point particle in the novel approach of proper mass varying under Minkowski force action. The motivation and objective of this work are twofold: first, to show how the gravitational force can be included in the Special Relativity Mechanics framework, and, second, to investigate possible consequences of the revision of conventional proper mass concept (in particular, to clarify a proper mass role in the divergence problem). It is shown that photon motion in the gravitational field can be treated in terms of massless refracting medium, what makes the gravity phenomenon compatible with SR Mechanics framework in the variable proper mass approach.

Specifically, the problem of point particle in the spherical symmetric stationary gravitational field is studied in SR-based Mechanics, and equations of motion in the Lorentz covariant form are obtained in the relativistic Lagrangean problem formulation. The dependence of proper mass on potential field strength is derived from the Euler-Lagrange equations as well. One of new results is the elimination of conventional 1/r divergence, which is known to be not removable in Schwarzschild gravitomechanics. Predictions of particle and photon gravitational properties are in agreement with GR classical tests under weak-field conditions; however, deviations rise with potential field strength. The conclusion is made that the approach of field-dependent proper mass is perspective for development of SR gravitational mechanics and further studies of gravitational problems.

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.

Similar content being viewed by others

References

  1. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, San Francisco (1973)

    Google Scholar 

  2. Brans, C.H.: Gravity and tenacious scalar fields. arXiv: ge-qc/9705069 v1 (1997)

  3. Rovelli, C.: Quantum Gravity. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  4. Smolin, L.: Three Roads to Quantum Gravity. Basic Books, New York (2001)

    MATH  Google Scholar 

  5. Smolin, L.: The Trouble with Physics: The Rise of String Theory, the Fall of a Science. Houghton Mifflin, Boston (2006)

    Google Scholar 

  6. Radiation reaction in general relativity. CGWP Workshop, Penn State University, 24–30 May (2002)

  7. Detweiler, S., Whiting, B.: Self-force via Green’s function decomposition. Phys. Rev. D 67, 024025 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  8. Diaz-Rivera, L.M., Messaritaki, E., Whiting, B., Detwieler, S.: Scalar field self-force effects on orbits about Schwarzschild black hole. Phys. Rev. D 70, 124018 (2004)

    Article  ADS  Google Scholar 

  9. Mino, Y.: From self-force-problem to radiation reaction formula. Class. Quantum Gravity 22, S717 (2005)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. Pound, A., Poisson, E., Nickel, B.: Limitations of adiabatic approximation to gravitational self-force. Phys. Rev. D 72, 124001 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  11. Poisson, E.: The gravitational self-force. arXiv:gr-qc/0410127 (2004)

  12. Burko, L., Harte, A., Poisson, E.: Mass loss by a scalar charge in an expanding universe. arXiv:gr-qc/0201020 (2002)

  13. Vankov, A.: Elimination of high-energy divergence in relativistic Lagrangean formulation of gravitating particle dynamics. arXiv: physics/0402117 (2004)

  14. Vankov, A.: On relativistic generalization of gravitational force. arXiv: physics/0611161 (2006)

  15. Synge, J.L.: Relativity: The Special Theory. North-Holland, Amsterdam (1965)

    Google Scholar 

  16. Synge, J.L.: Relativity: The General Theory. North Holland, Amsterdam (1964)

    Google Scholar 

  17. Moller, C.: The Theory of Relativity. The International Series of Monographs on Physics. Oxford University Press, Delhi (1972)

    Google Scholar 

  18. Nordstroem, G.: Reletivitatsprinzip and Gravitation. Phys. Z. 13, 1126–1129 (1912)

    Google Scholar 

  19. Nordstroem, G.: Trage und schwere Masse in der Reletivitatmechanik. Ann. Phys. 40, 856–878 (1913)

    Article  Google Scholar 

  20. Norton, J.D.: Einstein, G. Nordstroem, and early demise of scalar, Lorentz covariant theories of gravitation. Arch. Hist. Exact Sci. 45(1), 17–94 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. Byers, N.: E. Noether’s discovery of the deep connection between symmetries and conservation laws. In: Israel Mathematical Conference Proceedings, vol. 12 (1999)

  22. Bertolami, O., Paramos, J.: Astrophysical constraints on scalar field models. arXiv: astro-ph/0408216 (2004)

  23. Cui, H.-Y.: Discovery of quantum hidden variable. arXiv: physics.gen-ph/0711.1247v1 (2007)

  24. Hoyle, C.D., Heckel, B.R., Adelberger, E.G., et al.: Submillimeter test of the gravitational inverse-square law: a search for “large” extra dimensions. Phys. Rev. Lett. 86, 8 (2001)

    Article  Google Scholar 

  25. Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Pergamon, Elmsford (1975)

    Google Scholar 

  26. Goldstein, H.: Classical Mechanics. Series in Advanced Physics. Addison-Wesley, Reading (1950)

    Google Scholar 

  27. Goldstein, H., Poole, C., Safko, J.: Classical Mechanics, 3rd edn. Addison-Wesley, Reading (2001)

    Google Scholar 

  28. Fock, V.: The Theory of Space, Time, and Gravitation. Pergamon, Elmsford (1959). (Translated from the Russian by N. Kemmer)

    MATH  Google Scholar 

  29. Carroll, S.: Spacetime and geometry. In: Introduction to General Relativity. Pearson Higher Education (2003)

  30. Clifford, C.M.: Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  31. Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Relativity Theory. Willey, New York (1972)

    Google Scholar 

  32. Kostelecky, A.: CPT and Lorentz Symmetry. World Scientific, Singapore (2005)

    Google Scholar 

  33. Vankov, A.: On the de Broglie wave nature. Ann. Fond. Louis de Broglie 30(1), 15 (2005)

    MathSciNet  Google Scholar 

  34. Vankov, A.: Testing relativistic mass-energy concept in physics of gravity and electricity. Ann. Fond. Louis de Broglie 29(2), 1035 (2004) (The Special Issue dedicated to the 50th anniversary of the Yang-Mills, 1954, paper)

    Google Scholar 

  35. Vankov, A.: Mass, time, and clock (twin) paradox in relativity theory. arXiv: physics/0603168 (2006)

  36. Vankov, A.: On controversies in Special Relativity. arXiv: physics/0606130 (2006)

  37. Pound, R.V., Rebka, G.A.: Gravitational red-shift in nuclear resonance. Phys. Rev. Lett. 4(7), 337–341 (1960)

    Article  ADS  Google Scholar 

  38. Okun, L.B., Selivanov, K.G., Telegdi, V.L.: On the interpretation of the redshift in a static gravitational field. Am. J. Phys. 68, 115–119 (2000)

    Article  ADS  Google Scholar 

  39. Fishbach, E., Freeman, B.C.: Second-order contribution to the gravitational deflection of light. Phys. Rev. D 22(12), 2950 (1980)

    Article  ADS  Google Scholar 

  40. Callahan, J.J.: Geometry of Spacetime. Springer, Berlin (2000)

    MATH  Google Scholar 

  41. Shapiro, I.I.: Fourth test of General Relativity. Phys. Rev. Lett. 13, 789–791 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  42. Einstein, A.: The foundation of General Theory of Relativity. Ann. Phys. 49 (1916)

  43. Born, M.: Einstein’s Theory of Relativity. Dover, New York (1962)

    Google Scholar 

  44. Carmeli, M.: Classical Fields: General Relativity and Gauge Theory. Wiley, New York (1982)

    MATH  Google Scholar 

  45. Kenyon, I.R.: General Relativity. Oxford University Press, London (1991)

    Google Scholar 

  46. Ohanian, H.C., Ruffini, R.: Gravitation and Spacetime. Norton, New York (1994)

    MATH  Google Scholar 

  47. Blinnikov, S., Okun, L., Vysotsky, M.: Critical velocities in General Relativity. arXiv: gr-qc/0310020 (2003)

  48. Mashhoon, B.: Beyond gravitoelectromagnetism: critical speed in gravitational motion. Int. J. Mod. Phys. D 14(12), 2025 (2005)

    Article  MATH  ADS  Google Scholar 

  49. Vachaspati, T., Stojkovic, D., Kraus, L.M.: Observation of incipient black holes and information loss problem. Phys. Rev. D 76, 024005 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  50. Vachaspati, T., Stojkovic, D., Kraus, L.M.: arXiv: gr-qc/0609024 (2007)

  51. Robertson, S., Leiter, D.: Evidence for intrinsic magnetic moments in black hole candidates. Astrophys. J. 565, 447–454 (2002)

    Article  ADS  Google Scholar 

  52. Robertson, S., Leiter, D.: Astrophys. J. Lett. 576, L203 (2003)

    Article  ADS  Google Scholar 

  53. Loinger, A.: The black holes do not exist. arXiv: physics/0402088 (2004)

  54. Mazur, P., Mottola, E.: Gravitational condensate stars: an alternative to black holes. arXiv: gr-qc/0109035 v.5 (2002)

Download references

Author information

Authors and Affiliations

  1. IPPE, Obninsk, Russia

    Anatoli Andrei Vankov

  2. Bethany College, Lindsborg, KS, 67456-1895, USA

    Anatoli Andrei Vankov

Authors
  1. Anatoli Andrei Vankov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anatoli Andrei Vankov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vankov, A.A. On Relativistic Generalization of Gravitational Force. Found Phys 38, 523–545 (2008). https://doi.org/10.1007/s10701-008-9219-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-008-9219-z

Keywords

Search

Navigation