Goal of the course is to teach the physical motivations at the heart of the birth of general relativity as well as to make all students acquainted with the geometric and analytic techniques, necessary to learn the modern formulation of GR. Furthermore each student must become familiar with the main applications of the theory: gravitational waves, cosmology and black hole physics.
Course Prerequisites
It is required mastery of the concepts and tools learned during all the math courses of the batchelor studies in Physics as well as that of the physics courses on classical mechanics. The student is advised to take the course of Electrodynamics and Relativity.
Teaching Methods
All lectures will be given at the blackboard. On top of this, non compulsory home assignements will be given and they will be handled with the tools offered by Kiro
Assessment Methods
Written exam with exercises similar to those assigned during the course and oral exame on the topics discussed during the lectures
Texts
Lecture Notes available on the Kiro platform
Contents
The course will be focused on the following key points: 1) Physical motivations at the heart of general relativity and mathematical tools 2) Equivalence Principle (all different formulations) 3) Einstein's equations and their variational formulation 4) Newtonian limit and gravitational waves 5) Cosmology: homogeneous and isotropic metrics, Friedmann equations and their physical interpretation 6) Black hole Physics: Birkhoff theorem, Schwarzschild solution, geodesic motion of a test particle, event horizion and Kruskal extension. Rotating Kerr Black holes, ergosphere and Penrose processes.
