S. Carroll - Spacetime and geometry
B. Schutz - A first course in general relativity
Learning Objectives
Knowledge acquired: basic knowledge of general relativity (with reminders of special relativity)
Competence acquired: basic differential geometry techniques
Skills acquired: handling physical phenomena in the relativistic framework
Prerequisites
Calculus and vector calculus. Classical mechanics and electrodynamics. Basics of special relativity.
Teaching Methods
6 CFU
Class hours: 48
Further information
Office hours: in-person at the teachers' offices, during dedicated days/hours and/or by appointment. Additional office hours might be online, using the Webex platform (access via the Moodle-Webex connector).
Type of Assessment
Oral test, lasting approximately between 45 and 60 minutes. The exam starts with the exposition and discussion of a subject chosen by the student, among those discussed in class. Afterwards the student will be requested to discuss a different subject. The answers will be evaluated according to: understanding of fundamental physical aspects, ability to use a precise and rigorous language, ability to distinguish experimental facts from consequences that can be derived from these facts, ability to apply general results to specific examples, ability to reconstruct mathematical proofs discussed in class.
Course program
Reminders of special relativity:
Relativity principle. Minkowski spacetime. Lorentz transformations. Four-vectors and tensors. Relativistic kinematics and dynamics. Stress-energy-momentum tensor. Relativistic fluids. Covariant formulation of electromagnetism. Stress-energy-momentum tensor of matter and electromagnetic field.
General relativity:
Introduction to general relativity. Equivalence principle. Physical consequences of the equivalence principle: light bending and gravitational redshift. Experimental proofs of the equivalence principle and of its consequences. Differentiable manifolds. Vectors, tensors, metrics, differential forms, integration. Lengths and time intervals. Geodesics, covariant derivative, curvature tensor, Bianchi identities. Einstein field equations. Spherically symmetric solutions: Schwarzschild metric. Orbits in the Schwarzschild metric. Schwarzschild black holes. Experimental proofs of general relativity: light bending, advance of Mercury perihelion.