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Abstract <p>This study extends continuum mechanics methods to space-time, developing a mechanistic model of gravity. The gravitational field structure is established as a decomposition into four subfields: a 3D deviatoric (second-rank tensor) field, a 3D vector field, and two scalar fields. We propose a hypothesis of space-time’s transverse isotropy relative to the time coordinate unit vector. The physical properties of gravity in such a transversely isotropic space-time are shown to be governed by five ‘‘elastic moduli.’’ The two-level structure of the gravitational field and the wave equations are established. The first level is four gravitational subfields. They satisfy the coupled system of ‘‘4D equilibrium equations.’’ The second level—three primary gravitational fields, each defined by its own wave equation and having its own propagation velocity. The gravitational subfields are defined by linear combinations of differential operators over the primary gravitational fields.</p>

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Mathematical Model of Fields Structure in Mechanistic Theory of Gravitation

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • P. A. Belov,
  • S. A. Lurie

摘要

Abstract

This study extends continuum mechanics methods to space-time, developing a mechanistic model of gravity. The gravitational field structure is established as a decomposition into four subfields: a 3D deviatoric (second-rank tensor) field, a 3D vector field, and two scalar fields. We propose a hypothesis of space-time’s transverse isotropy relative to the time coordinate unit vector. The physical properties of gravity in such a transversely isotropic space-time are shown to be governed by five ‘‘elastic moduli.’’ The two-level structure of the gravitational field and the wave equations are established. The first level is four gravitational subfields. They satisfy the coupled system of ‘‘4D equilibrium equations.’’ The second level—three primary gravitational fields, each defined by its own wave equation and having its own propagation velocity. The gravitational subfields are defined by linear combinations of differential operators over the primary gravitational fields.