On Geometrization of Classical Fields (Model of Embedded Spaces)

TL;DR

This paper explores a geometric model of space-time that unifies gravitational and electromagnetic fields within a Finsler space framework, deriving Einstein and Maxwell equations and suggesting experimental tests for vacuum properties.

Contribution

It introduces a Finsler space-based geometrization of classical fields, deriving field equations and linking vacuum properties to cosmological constants.

Findings

Derivation of Einstein-type and Maxwell-type equations from the model

Identification of the vacuum's role in determining the cosmological constant

Proposal of experimental methods to verify electromagnetic vacuum effects

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.