Geometric Electrodynamics: Source Self-Consistency, Foundations, and Unification of Electromagnetic and Gravitational Phenomena

Building on a previously proposed coupling between the Maxwell tensor and the Riemann‑Christoffel curvature tensor [Ann. Phys. 465, 169661 (2024)],[i] this manuscript develops the conceptual and foundational implications of that framework, with particular emphasis on source self‑consistency and the unification of electromagnetic and gravitational source terms. The theory eliminates the need for externally introducing charge and mass and instead defines these quantities self-consistently in terms of the theory’s fundamental fields. By construction, all solutions of the theory satisfy the equations of Classical Electrodynamics identically. This approach highlights a conceptual ambiguity in the merger of Classical Electrodynamics and General Relativity, where the standard merger can admit multiple, potentially inequivalent local definitions of mass density. Here, by enforcing source self-consistency, the geometric framework provides a unified and intrinsic foundation for both charge and mass, ensuring compatibility across all equations of motion. Notably, the global symmetries of the theory lead to the emergence of antimatter and dictate its behavior in electromagnetic and gravitational fields, in agreement with classical expectations. Despite the nontrivial integrability conditions imposed by the geometric coupling, exact particle‑like and radiative solutions are presented which illustrate the unification of electromagnetic and gravitational phenomena and demonstrate the constraints imposed by the geometric structure. The results suggest new directions for foundational research, emphasizing the role of internal logical consistency in classical field theory and its potential implications for outstanding problems such as the equivalence principle and the nature of dark matter.