Construction of a Geometry in Relativity

Presentation of this approach This study lies halfway between mathematics and physics. It is not about reflecting on physics in the theory of Relativity. This physics has been perfectly known and verified for over a century. We fully respect it. It is also not about constructing a new mathematical theory but simply using mathematical tools, which are also perfectly known, to attempt a less analytical and more geometric approach. Analytical calculus, widely used in the geometry of Relativity, often yields numerical results that are challenging to interpret geometrically. What we aim to demonstrate is, on the one hand, that geometry in Relativity can be approached through an entirely geometric perspective, independent of physics, with a completely geometric representation that allows us to bypass tensor calculus in linearly accelerated reference frames, significantly reducing the need for analytical calculations. On the other hand, we want to show that the structure of space is more complex than the perception we have of it in the Euclidean reference frame.