As textbook, we will use?
S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Addison Wesley (2004).
The detailed curriculum is defined by the lectures and exercises, but approximate references to the book is given below.?
The following is a very tentative plan for what we will cover in the course (week numbers ?refer to teaching weeks, not calendar weeks)
| Weeks | Topics | Chapters is the book |
| 1 | Introduction. The equivalence principle. Introduction to manifolds | 2.1-2.3 |
| 2-4 | Differential geometry. Curvature | 2 and 3 |
| 5 | Einstein field equations | 4 |
| 6-7 | Spherically symmetric fields | 5 |
| 8-10 | Black holes and relativistic stars | 5 and 6 |
| 11-12 | Gravitational waves | 7 |
| 13-15 | Cosmology | 8 |
The plan will likely be revised during the semester. Below, I will give a more detailed description for each week as we proceed.?
Week 1 (19/1-23/1)
Introduction and the equivalence principle. Curvature from the equivalence principle. Introduction to manifolds.?
Exercises for the first week (solution) . To be discussed on Tuesday 20/1. To get best benefit from the problem solving class, try to solve the problems before you come.?
In addition there will be a discussion problem (solution) which will be given at the start of the class.?
Week 2 (26/1-30/1)
Tangent vectors to manifolds. Vectors and tensors. Metric tensor. Geodetic curves.?
Exercises week 2. (solution). ?To be discussed on Tuesday 27/1. To get best benefit from the problem solving class, try to solve the problems before you come.
In addition there will be a discussion problem (solution) which will be given at the start of the class.
Week 3 (2/2-6/2)
Covariant derivatives and parallel transport. Christoffel symbols.?
Exercises week 3. (Solutions) To be discussed on Tuesday 3/2. To get best benefit from the problem solving class, try to solve the problems before you come.
Week 4 (9/2-13/2)
Riemann normal coordinates. Riemann curvature tensor. Energy-momentum tensor.
Exercises week 4. ?(Solutions) To be discussed on Tuesday 10/2. To get best benefit from the problem solving class, try to solve the problems before you come.
Discussion problem for week 4, which will be given at the start of the class.
Week 5 (16/2-20/2)
Einstein field equations. Einstein-Hilbert action
Note that there is no lecture on Thursday 19/2
Exercises week 5. To be discussed on Tuesday 17/2. To get best benefit from the problem solving class, try to solve the problems before you come.
Week 6 (23/2-27/2)
Energy-momentum tensor. Birkhoff's theorem. Schwartzschild metric.?
Exercises week 6. (Solutions) To be discussed on Tuesday 24/2. To get best benefit from the problem solving class, try to solve the problems before you come.
Week 7 (2/3-6/3)
Killing vectors and conserved quantities. Geodetic curves in the Schwartzschild spacetime. Perihelion precession and light deflection.?
Exercises week 7. ?(Solutions) To be discussed on Tuesday 3/3. To get best benefit from the problem solving class, try to solve the problems before you come.
Discussion problem for week 7, which will be given at the start of the class.
Week 8 (9/3-13/3)
Black holes. Causal structure. Horizons. Conformal diagrams.?
Exercises week 8. ?(Solutions) To be discussed on Tuesday 10/3. To get best benefit from the problem solving class, try to solve the problems before you come
Discussion problem for week 8, which will be given at the start of the class.
Week 9 (16/3-20/3)
General black holes. Kerr metric horizons and singularity. Ergosphere and Penrose process.?
Exercises week 9. To be discussed on Tuesday 17/3. To get best benefit from the problem solving class, try to solve the problems before you come
Discussion problem for week 9, which will be given at the start of the class.
Week 10 (23/3-27/3)
Formation of black holes. Hawking radiation. Relativistic stars
Exercises week 10.(solutions) To be discussed on Tuesday 24/3. To get best benefit from the problem solving class, try to solve the problems before you come
Week 11 (6/4-10/4)
Linearized field equations and gravitational waves.?
No lecture on Monday 6/4 because it is still Easter vacation.?
We have no dedicated problem set for this week, but will have a general Q&A session on Tuesday to ask about anything you like and previous weeks' problem in particular if you need to catch up. If you want Tim to be extra prepared on something, send him an email in advance with your questions. Otherwise just come and ask.?
Week 12 (13/4-17/4)
Motion of test particles in gravitational waves. Sources of gravitational waves.
Exercises week 12. To be discussed on Tuesday 14/4. To get best benefit from the problem solving class, try to solve the problems before you come
Discussion problem for week 12, which will be given at the start of the class.
Week 13 (20/4-24/4)
Gravitational waves.?
Exercises week 13. To be discussed on Tuesday 21/4. To get best benefit from the problem solving class, try to solve the problems before you come
Discussion problem for week 13, which will be given at the start of the class.
Week 14 (27/4-1/5)
Detection of gravitational waves. Cosmology
Exercises week 14. To be discussed on Tuesday 28/4. To get best benefit from the problem solving class, try to solve the problems before you come
Discussion problem for week 14, which will be given at the start of the class.
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