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. 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. 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)
Birkhoff's theorem. Schwartzschild metric. Geodetic curves in the Schwartzschild spacetime.
Exercises week 6. 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)
Experimental tests: Perihelion precession and light deflection. Killing vectors and conserved quantities.?
Exercises week 7. To be discussed on Tuesday 3/3. To get best benefit from the problem solving class, try to solve the problems before you com
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