El modelo matemático del espacio-tiempo

Resumen

This paper intends to offer an introduction, as self-contained as possible, to the model of manifold proper to the space-time of macroscopical (classical) Physics. Starting from an elementary level, the first part brings forth a heuristic introduction to the concept of a smooth manifold, beginning from the intuitively simple concepts of curves and surfaces in R[raised to 3]. In the second part space-time is strictly defined in terms of a C[raised to infinite] manifold and of certain structures (connections, metrics) which can be added thereto. As a sequel of this study, a brief discussion is developed about the possible types of space-time that may play the role of local models of the Universe. Further, a comment is made on whether microscopical Physics (fractals, strange attractors, quantum gravity) may need or not a broader concept of space-time than that of a locally ordinary space R[raised to 4] furnished by a C[raised to infinite] manifold, owing to recent results by Freedman and Donaldson (1983) which demonstrate the existence of exotic or false R[raised to 4], upon which it has been shown that they constitute an infinite non countable set.