This paper introduces a novel formulation of the Schwarzschild metric as a solution to the Einstein field equations by incorporating a generalized potential compatible with the units of gravitational potential. This unified potential framework integrates gravitational, inertial, electric, and magnetic potentials into a single scalar quantity. By focusing on the radial component of the Riemann curvature tensor, we establish a direct connection between curvature, the field, and an effective refractive index emerging from the field's presence. This refractive index reinterprets curvature beyond traditional spacetime geometry, shaping the medium’s geometry and influencing particle and wave trajectories similarly to light propagation in inhomogeneous media. The generalized potential also establishes a mathematical bridge between electromagnetism and gravity, suggesting that electric charge gives rise to both electric and gravitational fields. This unified classical approach yields a field equation that captures the coupled behavior of these interactions, offering a new perspective on the unification of fundamental forces.