Introduction to general relativity

A.Y. 2021/2022
6
Max ECTS
48
Overall hours
SSD
FIS/02
Language
Italian
Learning objectives
This class represents an introduction to the theory of general relativity (GR). It starts with an introduction to differential geometry, the language in which GR is written. After that, the Einstein field equations are derived heuristically, and are finally solved in certain contexts, such as spherical symmetry (leading to the Schwarzschild solution), gravity waves and cosmology
Expected learning outcomes
At the end of the course the student is expected to have the following skills:
1. Profound knowledge of differential geometry;
2. Knows the Einstein field equations and their Newtonian limit;
3. Is able to solve the Einstein equations in a context with enough symmetry;
4. Knows the physics of the Schwarzschild solution and the classical tests of GR;
5. Knowledge in modern cosmology.
Course syllabus and organization

CORSO A

Responsible
Lesson period
First semester
More specific information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation
Course syllabus
Introduction to differential geometry, special relativity, Einstein equations, Schwarzschild geometry, linearized Einstein equations, Newtonian limit, gravity waves, black holes, FLRW cosmology.
Prerequisites for admission
Basics of special relativity, Maxwell equations, classical mechanics.
Teaching methods
Blackboard lectures, tutorials with exercises
Teaching Resources
My lecture notes, well-known textbooks by Carroll, Wald, Straumann, Weinberg, MTW,...
Assessment methods and Criteria
Oral examination
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 6
Lessons: 48 hours
Professor: Klemm Silke

CORSO B

Responsible
Lesson period
Second semester
In-person classes could be suspended due to (COVID-19 related) capacity and/or distancing restrictions on campus facilities. In this case classes will continue remotely, using the zoom platform.
Course syllabus
First part ( ~ 12 hours) : The physics of the equivalence principlel; brief recap of Special Relativity; Classical tests of GR

Second part (~12 hours): Differential geometry: Differential manifolds, tangent and cotangent space, tensor analysis, differential forms, (pseudo-)Riemannian manifolds, linear connections, curvature.

Third part (~ 24 hours): Einstein's Equations, Schwarzschild solution and black holes, FLRW cosmology, gravitational waves.
Prerequisites for admission
Knowledge of special relativity and classical mechanics. Prior knowledge of differential geometry is not expected.
Teaching methods
Attendance is highly recommended.
Traditional blackboard lectures. Lecture notes will be made available.
Homeworks solved at home and in class during the semester.
Teaching Resources
- David Tong's lectures - http://www.damtp.cam.ac.uk/user/tong/gr.html (mainly)
- S. Weinberg, "Gravitation and Cosmology"
- J. Hartle, "An introduction to Einstein's general relativity
Assessment methods and Criteria
Open book written exam and oral exam. Oral exam reserved to those who scored 18/30 or more at the written exam.
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 6
Lessons: 48 hours
Professor: Castorina Emanuele