A Geometric Model of Electromagnetic Interaction Based on the Volumetric Curvature of Space

This work presents a hypothetical geometric model in which electric charge and electromagnetic interaction are interpreted as consequences of localized volumetric deformation of space. Instead of introducing electric charge as a primitive entity, the model starts from a local linear deformation coefficient of space, denoted by alpha, and defines the volumetric curvature intensity as Delta K_v = 1 − alpha^3. A charged source is modeled as a localized spherical region with constant internal volumetric curvature intensity and an external compensating deformation.

The external distribution is derived from a variational argument. A scalar volume-change function Delta V(r) is introduced and, in the external region, satisfies Laplace’s equation. This leads to an external curvature-intensity profile proportional to r^(-4). The geometric charge is then defined as an integral characteristic of the external curvature flux, through the divergence of a radial vector field associated with this deformation.

The interaction between two non-overlapping spherical sources is constructed using a rationalized bilinear interaction functional. The leading term of the resulting force has the Coulomb form. Comparison with the standard Coulomb law relates the geometric stiffness, or energy density, of space to the electric constant. A magnetism-like interaction is interpreted as a consequence of moving geometric sources: the motion of the associated deformation produces an energy flux, and the corresponding momentum flux is obtained by division by c^2.

The model also interprets rest mass as the creation energy required to form the full deformation profile of a charged source. The proposed approach is not intended as a completed theory, but as an exploratory mathematical–physical framework for discussing charge, mass, and electromagnetic interaction.