This paper deals with the generalization of the linear theory of the unification of gravitational and electromagnetic fields using 4-dimensional gauge symmetry in order to solve the contradictions from the Kaluza-Klein theory’s unification of the gravitational and electromagnetic fields. The unification of gravitational and electromagnetic fields in curved space-time starts from the Bianchi identity, which is well known as a mathematical generalization of the gravitational equation, and by using the existing gauge symmetry condition, equations for the gravitational and electromagnetic fields can be obtained. In particular, the homogeneous Maxwell’s equation can be obtained from the first Bianchi identity, and the inhomogeneous Maxwell’s equation can be obtained from the second Bianchi identity by using Killing’s equation condition of the curved space-time. This paper demonstrates that gravitational and electromagnetic fields can be derived from one equation without contradiction even in curved space-time, thus proving that the 4-dimensional metric tensor using the gauge used for this unification is more complete. In addition, geodesic equations can also be derived in the form of coordinate transformation, showing that they are consistent with the existing equations, and as a result, they are consistent with the existing physical equations.
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