The kinematic space of special relativity and its hyperbolic geometry - Pereira, Rafael Ferreira (2021)
The classifying space of inertial reference frames in special relativity is naturally hyperbolic. There is a remarkable interplay between central elements of hyperbolic geometry and those of special relativity which, to a certain extent, have already been observed in the past that we present and further discuss in this dissertation. We aim at a geometrization of special relativity at the level of kinematic space by giving to physical concepts/phenomena purely geometric definitions/descriptions. In this way, the differences between special relativity and classical mechanics can be seen as a manifestation of the distinct geometric natures of their kinematic spaces. The dissertation has 4 chapters; the first two present some of the prerequisites, as well as a little bit of the history that culminated in the preprint that constitutes Chapter 4. This arXiv preprint, submitted for publication, contains the main results of the dissertation. In Chapter 3, we briefly discuss gyrovector spaces which constitute another algebraic framework to deal with hyperbolic geometry and special relativity.