The Intrinsic Energy Equation: Beyond the c Boundary through Volterra Integral Modeling

This paper introduces a novel derivation of the Einstein classic energy equation, termed “Intrinsic Energy Equation”, which express energy as an explicit argument independent of mass or external space-time coordinates. The present research aims to find an energy equation which locally admits on [0, c) as a solution Einstein's old formula 𝐸 = 𝑚𝑐! for energy but which is valid on R. Similarly, the equation sought must contain energy exclusively as an explicit term and not mass or space. The equation found will be called the "Intrinsic Energy Equation". Thus, we provide a global solution valid on R that eliminates the relativistic singularity at the speed of light. We also studied the energy space generated during the movement of a mobile as well as its potential. Then we briefly studied the form of this equation in R" , as well as its impact in certain particular cases on the Minkowski metric. Aim of this paper: “The End of Singularity" The Einsteinian limit was never an immutable law of nature, but a symptom of an incomplete metric. By formulating the Intrinsic Energy Equation, as we will see, we are replacing the 'infinite wall' with a finite transition. We show that the universe does not fall apart at the speed of light; rather, it changes its language. This paper provides the dictionary for a new language, opening the door to a physics in which the light barrier is not a final destination, but a gateway to new horizons. NOTE: Experimental data modelling is also provided as much as we could on virtual models using AI Gemini for calculus (all data tables and graphics in this study are made using Gemini AI “Lab” as it pleases to call itself...). Numerical simulations using Picard iterations and Runge-Kutta methods confirm that energy remains finite at 𝑣 = 𝑐 offering new theoretical frameworks for high-energy particle physics and plasma stability in fusion reactors.