Lecture Notes on General Relativity

Abstract

We present a basic introduction to General Relativity prepared for a four-month, graduate level course in the École Polytechnique Fédérale de Lausanne (14 weeks). The students are assumed to be familiar with Classical Mechanics (Lagrangian formulation, conservation laws, etc. . . ) and Special Relativity, without any prior knowledge of Classical Field Theory. The notes are thought to be pedagogical and physically oriented. The ubiquitous tensors are introduced in the familiar context of classical mechanics and electromagnetism. The transition to curved spacetime is motivated by physical concepts such as the equivalence principle or the existence of tidal forces. Even though these notes are intended to be self-contained and comprehensible, they are just a short guide to the main aspects treated in the course and do not aim to replace any of the many outstanding textbooks/notes on the subject.