The empirical Tully-Fisher relationship for spiral galaxies has been the subject of study for many years. The flat character of the rotation speed curves of galaxies and the need for the existence of dark matter to explain them made it even more difficult to find a theoretical foundation between the fourth power of the rotation speed of stars and their luminous mass or baryonic mass, that is, without dark mass, which would serve to demonstrate the relationship that R. Brent Tully and J. Richard Fisher found in 1977 for spiral galaxies and which is very useful for calculating various astronomical calculations. was until now physically unprovable.In this report we have demonstrated the Tolly-Fisher relationship using generalized relativity and applying it to a new energetic model of a galaxy. To achieve this, we use the Sérsic luminosity profiles as an estimate of baryonic mass and our new galaxy model to calculate the curvature of space-time within the galactic volume, subsequently deriving the acceleration experienced by the stars. The results show that this acceleration gives rise to a uniform velocity for each star, regardless of its position. as long as these are at a distance less than the effective radius. Furthermore, we have obtained a proportionality relationship between the luminosity of the galaxy and the fourth power of the rotation speed of the stars - the Tully-Fisher relationship - for spiral galaxies, which until now had been purely empirical.