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DIEGO TRANCANELLI
Professore Associato
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Fisica
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Insegnamento: Relativity
Physics - Fisica (Offerta formativa 2022)
Obiettivi formativi
General Relativity describes gravitational interactions from terrestrial to cosmological scales and is one of the best and most tested physical theories at our disposal.
The aim of this course is to provide students with a basic introduction to this theory (as well as a review of Special Relativity), in particular for what concerns the basics of differential geometry, the derivation of the Einstein equations and the analysis of their most interesting and fascinating solutions: black holes. The final part of the course will cover basic aspects of cosmology.
This is a fundamental course for all students interested in a theoretical curriculum.
Prerequisiti
Requirements. The mathematical knowledge of the three-year curriculum in physics (calculus, geometry, mathematical methods of physics). Elements of special relativity as developed in the courses of general physics.
An effort will be made to review these prerequisites when needed.
Programma del corso
The course consists of 24 2-hour long lectures, including some exercise sessions.
Topics to be covered include:
1. Special relativity
2. Tensor algebra and tensor calculus
3. Curvature
4. The principles of relativity, Einstein equations
5. Classic experimental tests
6. Black holes
7. Isometries and charges in general relativity
8. Linearized gravity and gravitational waves
9. Basics of cosmology
10. Black hole thermodynamics and elements of quantum gravity
Metodi didattici
The course is made of 48 hours of lectures and some sessions of proposed exercises. Some of them are homework and some will be solved in class.
Testi di riferimento
B.F. Shutz, "A first course in general relativity", Cambridge University Press.
R.M. Wald, "General Relativity", The University of Chicago Press.
S. Carroll, "Spacetime and geometry", Cambridge University Press.
A. Zee "Einstein gravity in a nutshell", Princeton Univ. Press.
Verifica dell'apprendimento
The grade will be based on an oral exam over all the program covered in the course and on the correction of a homework set distributed during the semester and due one week before the chosen date for the oral exam.
Risultati attesi
This course is designed for the first-year students of the Master Course in physics. The aim is to offer the basic concepts and tools of relativity (special and general), also in view of possible further studies.
Knowledge and Understanding.
At the end of the course the student will own the elements of special and general relativity and a view on the modern attempts to reach a quantum theory of gravitation; connections to cosmology will also be treated.
Applying Knowledge and Understanding.
The gained knowledge must allow the reading of advanced textbooks and research papers.
Making judgements.
The student should own, at the end of the course, the ability to use and to choose the methods to solve problems in general relativity and cosmology and to transfer to different fields the mathematical tools developed in this theory.
Communicating Skills.
To learn and to present the description of physical problems with the language and the methods of general relativity e communicate the basic knowledge.
Learning Skills.
The student, with this course, will be able to read, discuss and understand the topics in differential geometry, relativity, and cosmology, which are required for consulting, researching and developing technological applications in the field of modern physics.