On Geometrization of Classical Fields (Model of Embedded Spaces)

The possibility of geometrization of the gravitational and electromagnetic 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 on 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 and 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 a relic electric charge. A study of the gauge structure of the presented theory is postponed to the future.