General relativity in flat space-time

Einstein general relativity (GR) can be formally represented by a Lagrangian in a flat Minkowski space-time where light speed is not a universal constant and vanishes at the horizon of black holes. These appear as virtual singularities where no matter or energy can enter. We revisit the fundamental concepts of GR. Due to the principle of mass-energy equivalence, certain physical quantities, such as rest mass-energy, time, and light speed, must be rescaled according to the gravitational potential. We obtain a Lagrangian for a static gravitational potential (called germinal) different from the Schwarzschild Lagrangian but with the same black hole singularity. We develop a method that transforms a germinal Lagrangian into a fully relativistic Lagrangian. Then, the electrostatic Lagrangian becomes the well-known electromagnetic Lagrangian. The same method shows that the obtained germinal Lagrangian of gravitation generates a fully relativistic Lagrangian where gravitation is represented by a relativistic 4×4 tensor potential related to the Einstein stress-energy tensor. This theory is not equivalent to GR. In the weak gravitation limit, the Lagrangian generated by a stationary source only depends on a four-potential formally identical to that of the Heaviside theory of gravitation but different. As an application, we use this result in a simple model explaining the observed anomalies in the galaxy's stellar velocities without requiring hypothetical dark matter.