On the Unified Elastodynamics of Physical Vacuum: Extension of Maxwell's Equations to Gravitational Gradients, Non-Linear Field Coupling, and the Hydrostatic Origin of Inertia

Modern theoretical physics exhibits an unresolved dualism: classical electrodynam- ics posits linear wave propagation within a passive, metric-free Minkowski background, whereas General Relativity models gravitation through geometric space-time curva- ture. This methodological separation produces non-physical singularities at point sources, enforces unobserved ad-hoc parameters (the non-baryonic dark sector) to salvage as- trophysical observations, and forbids mutual cross-coupling between magnetic field gradients and photon geodesics in vacuo. In this paper, we formalize a unified elasto- dynamic framework wherein the physical vacuum is treated as an active, pre-stressed mechanical continuum characterized by finite elastic bulk modulus Kv , shear rigidity Gv , and background hydrostatic stress P0. We extend Maxwell’s equations into a five- equation closed system (“Novak equations”) wherein electric permitivity ε and mag- netic permeability µ are no longer invariant constants, but constitutive state tensors determined by the local stress tensor and hydrostatic gradient. Under this formula- tion: (1) transverse shear strains correspond to electromagnetic wave propagation, while divergence of the isotropic hydrostatic pressure gradient produces the Newton- Poisson gravitational acceleration without spatial warping; (2) deflection of light by intense magnetic gradients and by gravitational bodies is governed by an identical variable-index refractive law n(⃗r) = ε(⃗r)µ(⃗r); (3) the absence of isolated magnetic monopoles is proven as an intrinsic topological identity of continuous shear vorticity (∇ ·⃗ B ≡ 0); and (4) finite yield elasticity naturally regularizes Coulomb and gravitational central singularities.