RELATIVITY
Academic year and teacher
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- LUCA PAGANO
- Credits
- 6
- Didactic period
- Secondo 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.
The main acquired knowledge will be:
Curvature of spacetime.
Einstein field equations.
Black hole solutions.
Gravitational waves and emission of gravitational radiation. Prerequisites
- Familiarity with special relativity, whose main topics will be nonetheless discussed.
Course programme
- The formalism of Special Relativity, Minkowski spacetime, Lorentz transformations, vectors, and tensors (6 hrs)
The linear approximation, Variational principle, Geometric interpretation (6 hrs)
Applications of the linear approximation, Field of a spherical mass, Gravitational time dilation, Deflection of light, Einstein ring, Lense-Thirring effect (6 hrs)
Gravitational waves, Interaction of particles with a gravitational wave, Emission of gravitational radiation, Detectors of gravitational radiation (8 hrs)
Riemannian geometry, General coordinates, Covariant derivative, Riemann curvature tensor, Isometries of spacetime (10 hrs)
Einstein’s gravitational theory, Schwarzschild solution, Propagation of light, Perihelion precession (10 hrs)
Black holes, Singularities and pseudosingularities, Kruskal coordinate, maximally extended solution, Kerr solution (8 hrs) Didactic methods
- The course is organized in several lectures that will cover all required topics. Worked out examples will also be discussed, to support the learning process.
Learning assessment procedures
- 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 and the knowledge 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
- Ohanian and Ruffini, Gravitation and Spacetime, Cambridge University Press
Sean Carroll, Spacetime and Geometry: Introduction to General Relativity, Prentice Hall
Notes will be handed over.
