Introduction to General Relativity
A.Y. 2020/2021
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.
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.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Lectures will be administrated remotely.
Course syllabus
First half (about 24 hours): Brief summary of special relativity; introduction to differential geometry: Differential manifolds, tangent and cotangent space, tensor analysis, differential forms, (pseudo-)Riemannian manifolds, linear connections, curvature.
Second half: Einstein equations, Schwarzschild solution, classical tests of GR, black holes, FRW cosmology, gravitational waves.
Second half: Einstein equations, Schwarzschild solution, classical tests of GR, black holes, FRW cosmology, gravitational waves.
Prerequisites for admission
Knowledge of special relativity and classical mechanics.
Teaching methods
Attendance is highly recommended.
Traditional blackboard lectures. Lecture notes will be made available.
Homeworks solved in class during the semester.
Traditional blackboard lectures. Lecture notes will be made available.
Homeworks solved in class during the semester.
Teaching Resources
- David Tong's lectures - http://www.damtp.cam.ac.uk/user/tong/gr.html
- S. Weinberg, "Gravitation and Cosmology"
- J. Hartle, "An introduction to Einstein's general relativity"
- S. Weinberg, "Gravitation and Cosmology"
- J. Hartle, "An introduction to Einstein's general relativity"
Assessment methods and Criteria
Homeworks, 3x.
Written exam. Grade: #/30
Oral exam reserved to those who scored 18/30 or more at the written exam.
Written exam. Grade: #/30
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
Professor(s)