On the Nordtvedt effect in Minkowski spacetime with nonlinear connection

  • Authors

    • Kostadin Trenčevski Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University in Skopje
    • Emilija Celakoska Faculty of Mechanical Engineering, Ss. Cyril and Methodius University in Skopje
    2017-11-06
    https://doi.org/10.14419/ijamr.v6i4.7617
  • Lunar Laser Ranging, Equivalence Principles, Earth-Moon Distance, Gravitation.

  • The Lunar Laser Ranging (LLR) experiment provided precise data which brought the possibility to make more stringent conclusions for the foundations of gravitational theories, i.e. the Equivalence Principles. Beside some effects of non - gravitational origin, the LLR data was fitted with the well-known gravitational effects such as the apsidal and geodetic precessions, the time delay, etc. The Nordtvedt effect in General Relativity (GR) vanishes, while the LLR experiment data of the Earth-Moon distance and the laboratory experiments with experimental bodies made of different chemical compositions measured a variation of distance in millimeters. According to the mathematical model of gravitation in Minkowski space endowed with a nonlinear connection we obtained a result closer to the experimental measurements. More precisely, we obtained a difference of 0.17 mm (or 0.28 mm, depending on the value of the scaling factor) from the LLR measurements of the variation of the Earth-Moon distance, while the corresponding result in GR makes a difference from the LLR measurements of 5.7 mm. The gravitational theory with nonlinear connection in Minkowski space gives the same results for the confirmed GR effects, nevertheless it yields some additional variations of the distance concerning the Nordtvedt effect.

  • References

    1. [1] Adelberger, E.G., New tests of Einstein's equivalence principle and Newton's inverse-square law. Classical and Quantum Gravity, Vol.18, No.3, (2001), pp. 2397-2405, available online: http://iopscience.iop.org/article/10.1088/0264-9381/18/13/302

      [2] Fahnline, D.E., A covariant four-dimensional expression for Lorentz transformations. American Journal of Physics, Vol.50, No.9, (1982), pp. 818-821, http://aapt.scitation.org/doi/abs/10.1119/1.12748

      [3] Matolcsi, T., Spacetime without Reference Frames. Akadémiai Kiadó, Budapest, (1993), pp: 156.

      [4] Nordtvedt, K., Lunar laser ranging, a comprehensive probe of post-Newtonian gravity, In: Ciufolini, I. et al (eds.) Gravitation. Villa Mondragone International School of Gravitation and Cosmology, Rome, (2002), pp: 97-113, http://cds.cern.ch/record/599495/files/ 0301024.pdf

      [5] Nordtvedt, K. and Vokrouhlicky, D. (1997), Recent progress in analytical modeling of the relativistic effects in the lunar motion. In: Wytrzyszczak, I.M., Lieske, J.H. and Feldman, R.A. (eds.) Dynamics and astronomy of the natural and artificial celestial bodies, Kluwer Academic Publishers, Dordrecht, pp. 205-214.

      [6] Nordtvedt, K., The relativistic orbit observables in lunar laser ranging. Icarus, Vol.114, (1995), pp. 51-62, https://doi.org/10.1006/icar.1995. 1042

      [7] TrenÄevski, K., One model of gravitation and mechanics. Tensor, Vol.53, (1993), pp. 70-82.

      [8] TrenÄevski, K., Celakoska, E. and Balan, V., Research of gravitation in flat Minkowski space, International Journal of Theoretical Physics, Vol.50, No.1, (2011), pp. 1-26, doi:10.1007/s10773-010-0488-x.

      [9] TrenÄevski, K. and Celakoska, E., Equations of motion for two body problem according to an observer inside the gravitational field. Journal of Dynamical Systems & Geometric Theories Vol.9, No.2, (2011), pp. 115-135, http://dx.doi.org/10.1080/1726037X.2011.10698596.

      [10] TrenÄevski, K. and Celakoska, E., Representation of geodesics near the Schwarzschild radius. Gravitation and Cosmology Vol.21, No.1, (2014), pp.93-103, doi:10.1134/S0202289315010132.

      [11] Will, C.M., Theory and Experiment in Gravitational Physics. Cambridge University Press, New York (1993), pp:185-190.

      [12] Will, C.M., The confrontation between General Relativity and Experiment. Living Reviews in Relativity, Vol.9, (2006), pp.3-100. doi: 10.12942/lrr-2014-4

      [13] Williams, J.G., Turyshev, S.G. and Boggs, D.H., Lunar laser ranging tests of the Equivalence principle with the Earth and Moon. International Journal of Modern Physics D, Vol.18, (2009), pp. 1129-1175, http://dx.doi.org/10.1142/S021827180901500X.

      [14] Williams, J.G., Turyshev, S.G. and Boggs, D.H., Progress in lunar laser ranging tests of relativistic gravity. Physical Reviews Letters Vol.93, (2004), pp. 261101, https://doi.org/10.1103/PhysRevLett.93. 261101

      [15] Williams, J.G., Turyshev, S.G. and Murphy, T.W. Jr., Improving LLR tests of gravitational relativity. International Journal of Modern Physics D, Vol. 13, (2004), pp. 567-582,

      http://dx.doi.org/10.1142/S0218271804004682.

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  • How to Cite

    Trenčevski, K., & Celakoska, E. (2017). On the Nordtvedt effect in Minkowski spacetime with nonlinear connection. International Journal of Applied Mathematical Research, 6(4), 130-134. https://doi.org/10.14419/ijamr.v6i4.7617