On Geometrization of Classical Fields (Model of Embedded Spaces)

Abstract: The possibility of geometrization of the gravitational and electro magnetic fields in 4D Finsler space (the Model of Embedded Spaces -- MES) is investigated. The model postulates a proper metric set of an element of distributed matter and asserts that space-time is a mutual physical embedding of such sets. The simplest MES geometry is constructed (its relativistic Finsler version) with a connection that depends of the properties of matter and its fields (torsion and nonmetricity are absent). The field hypothesis and the Least Action Principle of the matter-field system lead to Einstein-type and Maxwell-type equations, and their nonlinearity -- to the anisotropic field contribution to the seed mass of matter. It is shown that the seed matter plays the role of a physical vacuum of the Embedding determines the cosmological constant. In the special case of a conformal metric, the Maxwell-type equations reduce to the Maxwell equations themselves and a negative electromagnetic contribution. A possible experimental verification of this result is evaluated. The "redshift" effect in an electric field is also mentioned as a method for studying the vacuum and relic electric charge. A study of the gauge structure of the presented theory is postponed to the future.