Abstract
We address gravitation and inertia in the framework of a general gauge principle (GGP) which accounts for the gravitation gauge group G R generated by a hidden local internal symmetry implemented on the flat space. Following the method of phenomenological Lagrangians, we connect the group G R to a non-linear realization of the Lie group of the distortion G D of the local internal properties of six-dimensional flat space, M 6, which is assumed as a toy model underlying four-dimensional Minkowski space. We study the geometrical structure of the space of parameters and derive the Maurer–Cartan’s structure equations. We treat distortion fields as Goldstone fields, to which the metric and connection are related, and we infer the group invariants and calculate the conserved currents. The agreement between the proposed gravitational theory and available observational verifications is satisfactory. Unlike the GR, this theory is free of fictitious forces, which prompts us to address separately the inertia from a novel view point. We construct a relativistic field theory of inertia, which treats inertia as a distortion of local internal properties of flat space M 2 conducted under the distortion inertial fields. We derive the relativistic law of inertia (RLI) and calculate the inertial force acting on the photon in a gravitating system. In spite of the totally different and independent physical sources of gravitation and inertia, the RLI furnishes a justification for the introduction of the Principle of Equivalence. Particular attention is given to the realization of the group G R by the hidden local internal symmetry of the abelian group U loc=U(1) Y ×diag[SU(2)], implemented on the space M 6. This group has two generators, the third component T 3 of isospin and the hypercharge Y, implying Q d=T 3+Y/2, where Q d is the distortion charge operator assigning the number −1 to particles, but +1 to anti-particles. This entails two neutral gauge bosons that coupled to T 3 and Y. We address the rearrangement of the vacuum state in gravity resulting from these ideas. The neutral complex Higgs scalar breaks the vacuum symmetry leaving the gravitation subgroup intact. The resulting massive distortion field component may cause an additional change of properties of the spacetime continuum at huge energies above the threshold value.
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Ter-Kazarian, G. Gravitation and inertia; a rearrangement of vacuum in gravity. Astrophys Space Sci 327, 91–109 (2010). https://doi.org/10.1007/s10509-010-0282-5
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DOI: https://doi.org/10.1007/s10509-010-0282-5