The classical geometrization of the electromagnetism II

In a previous work C. A. Duarte, The classical geometrization of the electromagnetism, Int. J. Geom. Met. Mod. Phys. 12 (2015) 1560022, it was analyzed the geodesic equation of the general relativity theory, in which the electromagnetic interaction term contains the components of the electromagnetic tensor. The study pointed out that the electromagnetic field can be included in the geometry of the four-dimensional space-time, with a suitable space-time metric that contains the components of the four-vector electromagnetic potential. Presently, this work is recovered focusing on the requirement of Lorentz invariance of the metric. This requirement leads to including an additional term in the expression of the space-time interval that contains the contribution of the electromagnetism, separated from the bare gravitational term.