General Relativity (FYSS7320 9 PTS), SPRING 2022

General

Lecturer:
Kimmo Kainulainen
FL216
Lectures 56 h:
Mon 10.15-12.00 and Thu 14.15-16.00
YNC 121 (Mon) and FYS3 (Thu)
Course time:
10.1.-7.14

Grading assistant
Pyry M. Rahkila

--
Excercises 28 h:
Thu 16.15-18.00 
YNC 121
2 exams
Exam 1: 4.3. Exam 2: 22.4
 

Registraation: through sisu, as usual.

Course Content

The course provides an introduction to General Relativity which is a classical theory of gravity. General Relativity describes gravity as curvature of the spacetime and it includes Newtonian gravity as the weak field limit. Topics included contain a brief review of special relativity, introduction to differential geometry and curved spacetimes, Einsteins equations and curvature, Schwartzschild solution for stars and black holes and gravitational waves if time allows. In particular, the course aims to provide the theoretical background and tools useful for lecture courses on cosmology

Learning outcomes

At the end of the course, students will be able to explain the basic concepts of special and general relativity and their differences. Students will be able to compute the transformation of tensor components under coordinate transformations and form covariant derivatives, compute distances between points of the spacetime using the metric as well as compute the connection coefficients and the curvature tensor from the metric. Students will be able to form the geodesics equations, understand their meaning and solve them in simple setups. Students will also be able to form Einstein equations by varying the action and understand their meaning as well as solve Einstein equations for a spherically symmetric, static, empty space outside a star (Scwartzschild) and compute orbits of test bodies and light and gravitational redshifts in the Schwartzschild space.

Source literature

Course follows most closely the excellent book by S.M. Carroll. In all, the most useful books for this course are, to my opinion (others exist and may be preferred by other people of course):

S.M. Carroll
Spacetime and Geometry (Addison Wesley 2004)
D. Tong
General Relativity
R. Wald
General Relativity
M. Nakahara
Geometry, Topology and Physics
 

In particular, I took the liberty provide lecture notes on general relativity by David Tong here. The original homepage of the notes is here . When on this page, go down the list and try to resist (or not!) the temptation to start reading the other (there are currently 20!) excellent lecture notes on theoretical physics provided by Professor Tong, free of charge!

I will follow, with very minor corrections, the handwritten lecture notes by Sami Nurmi. These notes are divided into 8 parts, which can be separately downloaded from the links below. Also, the weekly excercises will be provided in the links in the last table, as their time comes.

Lectures

Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7 Part 8

Complementary material on the section on parallel transport, covariant derivative and curvature can be found here

Excercises

Ex. 1 Ex. 2 Ex. 3 Ex. 4 Ex. 5 Ex. 6 Ex. 7 Ex. 8 Ex. 9 Ex. 10 Ex. 11 Ex. 12

Luennot

Linkit joihinkin alkupään luentojen tallenteisiin löytyvät täältä. Liitetiedoston avaaminen onnistuu vain polkuavaimella. Kurssilaiset saavat sen luennoitsiajlta.

Code

The simple mathematica code to compute the Christoffel connection coefficients and curvature tensors and scalars from the metric can be found here here.
Kimmo Kainulainen
Last edited: 10 January 2022