Gravitation and inertia; a rearrangement of vacuum in gravity

Abstract

We address the gravitation and inertia in the framework of general gauge principle (GGP) which accounts for gravitation gauge group GR generated by hidden local internal symmetry implemented on the flat space. Following the method of phenomenological Lagrangians, we connect the group GR to nonlinear realization of the Lie group of distortion GD of local internal properties of sixdimensional flat space M6, which is assumed as a toy model underlying four-dimensional Minkowski space. We study 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 infer the group invariants and calculate conserved currents. The agreement between 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 relativistic field theory of inertia, which treats inertia as distortion of local internal properties of flat space M2 conducted under the distortion inertial fields. We derive the relativistic law of inertia (RLI) and calculate inertial force acting on the photon in gravitating system. In spite of totally different and independent physical sources of gravitation and inertia, the RLI furnishes justification for introduction of the Principle of Equivalence. Particular attention is given to realization of the group GR by the hidden local internal symmetry of abelian groupimplemented on the space M6. This group has two generators, third component T 3 of isospin and hypercharge Y implying, 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 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 spacetime continuum at huge energies above the threshold value.

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“…Discussed gravitational theory is consistent with general relativity for available solar system observational verifications [10], which offers many opportunities to improve tests of relativistic gravity. Moreover, we rather shown that this agreement is satisfactory even up to the limit of neutron stars (see [9] and references therein).…”

“…The proposed theory explores a spontaneous breaking of gravitation gauge symmetry ( [18,9,10] and earlier references cited therein, which thoroughly discussed in [11,12]). Much use has been made of the language of fundamental geometric structure, that is, a distortion gauge induced fiber-bundle, incorporating with the spacetime deformation/distortionframework [12,19,20].…”

“…The nonlinear realization technique or the method of phenomenological Lagrangians (see [10] and references therein) provides a way to determine the transformation properties of fields defined on the quotient space. We treat the distortion group G D and its stationary subgroup H = SO(3), respectively, as the dynamical group and its algebraic subgroup.…”

“…The generators X A (54) of the group Q do not complete the group H to the dynamical group G D , therefore, they cannot be interpreted as the generators of the quotien space G D /H, and the distortion fields a A cannot be identified directly with the Goldstone fields arisen in spontaneous breaking of the distortion symmetry G D . These objections, however, can be circumvented, because, as it is shown by [10], the distortion group G D = Q × SO(3) can be mapped in a one-to-one manner onto the group G D = SO(3) × SO (3), which is isomorphic to the chiral group SU (2) × SU (2). The method of phenomenological Lagrangians is well known for this group.…”

“…The fundamental field is distortion gauge field (a) and, thus, all the fundamental gravitational structures in fact -the metric as much as the coframes and connections -acquire a distortion-gauge induced theoretical interpretation. We study the geometrical structure of the space of parameters in terms of Cartan's calculus of exterior forms and derive the Maurer-Cartan structure equations, where the distortion fields (a) are treated as the Goldstone fields [10].…”