2025/12/05 by Horoto, L., Scholtz, F. G.
Physics and Astronomy · #Quantum Electrodynamics and Casimir Effect #Relativity and Gravitational Theory #Cosmology and Gravitation Theories
paper · doi:10.48550/arxiv.2512.06050
We propose a reformulation of gravitation in which the gravitational interaction is treated as a genuine force rather than an inertial effect arising from spacetime geometry. Within this framework, the difference between the affine connection and a flat reference connection defines a tensor Kμαβ, identified as the gravitational field strength. This object cannot be eliminated by coordinate transformations, demonstrating that gravity possesses true physical degrees of freedom. The formalism introduces vector fields ξaμ that extend the notion of infinitesimal translations to curved spacetime and naturally yield a gauge-invariant field strength \mathfrakFξaμν. The dynamics of the gravitational field are governed by a Lagrangian of Yang--Mills type with an additional scalar degree of freedom ϕ2, corresponding to the Newtonian potential. In the limit of vanishing gravitational coupling \mathfrakg→0, the theory reduces to General Relativity, while for nonzero \mathfrakg it constitutes an SU(2)× U(1) gauge theory of gravity. The framework provides a unified description in which dark energy emerges as the self-interaction energy of the ϕ field, and dark-matter-like effects arise from the extended gravitational degrees of freedom. This formulation offers a consistent bridge between classical and quantum descriptions of gravity and clarifies the conceptual foundations of the gravitational interaction.