RELATIVITY
Academic year and teacher
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- Versione italiana
- Academic year
- 2015/2016
- Teacher
- PAOLO NATOLI
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- FIS/01
Training objectives
- This course aims at providing the basic principles of general relativity and its underlying geometrical framework. The student will acquire the main topics in the theory and the principal application of physical, astrophysical and cosmological relevance
Prerequisites
- Familiarity with special relativity, whose main topics will be nonetheless discussed.
Course programme
- Review of special relativity: Minkowski spacetime, Lorentz transformations, vectors and tensors (6 hours)
Gravity and geometry: curved manifolds, vectors and tensors on the manifold, metric tensor. Observables (6 hours)
Curvature, covariant derivatives, parallel transport, geodesics and their properties (6 hours)
Einstein equations, Lagrangian formulation (4 hours)
Scwarzschild metrics and its properties. Experimental evidence in support of GR: perihelion precession, light deflection (6 hours)
Scwarzschild black holes, Kruskal coordinates, maximally extended solution, fundamentals of astrophysical black hole properties (6 hours)
Perturbation theory: linearized gravity, gauge transformations, gravitational waves (6 hours)
Maximally symmetric universes, Robertson-Walker metrics, Friedmann equation and related expansion models (4 hours)
NB: quoted timings are estimates only. Didactic methods
- The course is organized in several lectures that will cover all required topics. Worked out examples and exercises will also be discussed, to support the learning process.
Learning assessment procedures
- Informal discussion before the final exam should help the student in gauging the comprehension level attained. The final exam is a colloquium, lasting about 45 minutes, usually divided between three questions. The exam will be aimed at verifying the competence level acquired, by means of discussions concerning the course material as well as specific examples of application of the theory. There is no written test.
Reference texts
- Sean Carroll, Spacetime and Geometry: Introduction to General Relativity, Prentice Hall
Notes will be handed over.
