A mathematical approach to general relativity theory

Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2014, Director: Carlos Currás BoschThe aim of this project is to outline the Special Relativity and the General Relativity theory, paying special attention to some mathematical concepts, such as Lorentz transformations and the Ricci tensor, which happen to be key points to this theory which revolutionated Physics in the beginning of last century. We assume that the reader have some previous mathematical knowledge, specially about Differential Geometry, and will therefore skip definitions and theorems regarding this area of Mathematics (such as the definition of connexion, Riemannian metrics or curvature). We shall give some notions of classical Physics in the first chapter, in order to look over them in Chapters 2 and 3 at light of Special Relativity and General Relativity theories, respectively