Energy metrics and their Ricci flows - Benenti, Sergio; Cardone, Fabio (Annals of Mathematics and Physics, 2024)
The framework of the Deformed Space-Time theory has been extended in the past from four to five dimensions, where the fifth coordinate is the energy exchanged by the interaction. In this theory, each fundamental interaction is described by an energy-dependent metric. This picture has been exploited in order to take care of the interaction behaviour both when Lorentz invariance holds and the spacetime is Minkowskian and when Lorentz is violated and must be recovered in a non-minkowskian spacetime. It has been successfully attempted to complete the pentadimensional metric of the four fundamental interactions calculating the fifth element of the metric corresponding to the fifth coordinate energy. The mathematical tool exploited is the method of the Ricci flow which gave the complete explicit form of the fifth element of the metric, answering in this way the question of "how the energy measure the energy" for each interaction, setting the electromagnetic interaction as the reference for the energy measure. In this sense it has been given meaning to the problem of the energy gauge for interaction, identifying the gauge with the fifth metric element. The consequences of the nuclear metamorphosis have been also examined for reaching the technological goal of a device stably producing this metamorphosis under the hadronic metric. The most valuable consequence is that in this pentadimensional picture, the old Einsteinian dream of a complete geometrization of the interactions is reached. The results achieved in the present work have allowed to design, build, and test of devices capable of exploiting the behavior of the fifth element of the metrics to obtain the production of electric charges directly from the nuclear metamorphosis of the matter.