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Subject: RELATIVITY (A.A. 2021/2022)

master degree course in PHYSICS – FISICA

Course year 2
Teaching units Unit Relativity
Theory and Foundations of Physics (lesson)
  • TAF: Compulsory subjects, characteristic of the class SSD: FIS/02 CFU: 6
Teachers: Diego TRANCANELLI
Exam type oral
Evaluation final vote
Teaching language Italiano
Contents download pdf download




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 cosmology and transfer also 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.

Admission requirements

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.

Course contents

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

Teaching methods

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. NOTE: The lectures and exercise sessions will happen either in presence or via remote learning depending on the evolution of the COVID-19 emergency.

Assessment methods

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. NOTE: The exams will happen either in presence or via web-conference depending on the evolution of the COVID-19 emergency.

Learning outcomes

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.


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.