General Relativity, spring 2012

53736 Yleinen suhteellisuusteoria (10 op)

Lecturer: Hannu Kurki-Suonio, office hour Mo 10-11, C328
Assistant: Matti Savelainen, C329

Lectures: Mo 14-16, Tu 14-16 (Physicum, A315)
Exercises: Th 16-18 (A315)

No lecture on Tuesday February 14th.

The lecturer and assistant can be contacted by e-mail at firstname.lastname(at)helsinki.fi

First lecture: January 23rd.
Language of instruction: English (unless everyone understands Finnish).
Register to the course in Weboodi. (Only registered students get their homework graded and receive course announcements by e-mail.)

Contents: Special relativity review. Vector and tensor fields. Manifolds and differential geometry. Field equations and curvature. Physics in the vicinity of a massive object. Black holes. Maximally symmetric spacetimes. Elements of cosmology. Cosmological perturbation theory.
Exams and grades: The grade is based both on the weekly exercises (20%) and on the exam (80%). You need to get about 45% of full points to pass the course (grade 1), and about 25% of full points to earn the right to try to pass the course in a General Exam (this should be done before the course is lectured again; registration for the General Exam is done on WebOodi). Otherwise the only way to get credit for the course is to take the course again.
Exercises: The homework problems are given out on Tuesdays. They appear here on the course web page (see below). You are supposed to do the homework and return them into the General Relativity "safe deposit box" (in 2nd floor A corridor) for grading before the following Monday lecture.
Textbook: S.M. Carroll, Spacetime and Geometry (Addison Wesley 2004). This book is in the reference library.
Notes by the lecturer will be made available.
I purchased my copy of Carroll's book from www.amazon.co.uk. Teppo got his from www.bookplus.fi. It is not necessary to buy the book; my lecture notes will cover the content of this course and you could also read Carroll's lecture notes (on which his book is based; the lecture notes are very good too, but they are shorter and less polished than the book) which are freely available on the net. However, I do recommend the book, at least for those students who plan to study theoretical physics further.
Some other literature:
Three classic texts:
S. Weinberg, Gravitation and Cosmology (Wiley 1972).
C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (Freeman 1973). (MTW)
R.M. Wald, General Relativity, (The University of Chicago Press 1984).
Two good short textbooks that do not cover all of the course, but are easy to read:
B.F. Schutz, A First Course in General Relativity (Cambridge 1985).
J. Foster and J.D. Nightingale, A Short Course in General Relativity, 2nd edition (Springer 1994, 1995), in the reference library. (FN)
Some more recent books, with a different approach:
J.B. Hartle, Gravity - An Introduction to Einstein's General Relativity (Addison Wesley 2003).
B. Schutz, Gravity from the Ground Up (Cambridge 2003).
Carroll's lecture notes:
S.M. Carroll, Lecture Notes on General Relativity (gr-qc/9712019).

Discussion:

(Jump further down for English)
Kurssin alussa on suppeamman (l. erikoisen) suhteellisuusteorian kertaus (missä yhteydessä esitellään osa yleisessä suhteellisuusteoriassa tarvittavista käsitteistä), mutta varsinaisesti kyseessä on yleisen suhteellisuusteorian kurssi. Suppeamman suhteellisuusteorian siis oletetaan olevan osallistujille jo ennestään tuttu.

Suositeltavat esitiedot: Matemaattiset apuneuvot I ja II, Suhteellisuusteorian perusteet, Mekaniikka, Elektrodynamiikka, Fysiikan matemaattiset menetelmät III. Fymm III:lla käsitelty differentiaaligeometria on yleisen suhteellisuusteorian perustyökalu. Käytettävät differentiaaligeometrian menetelmät kuitenkin kerrataan kurssilla, niin että Fymm III ei ole välttämätön esitieto.

This is the course in general relativity. The course begins with a review of special relativity (in order to introduce some of the tools needed in general relativity). The students are expected to have a background in special relativity already.

The recommended background includes mathematical methods (curvilinear coordinate systems, coordinate transformations, linear algebra, vectors and tensors, and differential geometry), classical mechanics, special relativity, and electrodynamics. Differential geometry (as well as some of the other math needed) will be reviewed in the course, so previous knowledge of it is not necessary.

Contents of the course

The material covered in this course will be roughly the same as in previous years. It corresponds to at least the following chapters and sections of Carroll: Spacetime and Geometry.
Chapter 1: Special Relativity and Flat Spacetime - entire chapter
Chapter 2: Manifolds - all sections except 2.7
Chapter 3: Curvature - all sections except 3.8 and 3.10
Chapter 4: Gravitation - sections 4.1, 4.2, 4.3, 4.5
Chapter 5: The Schwarzschild Solution - all sections except 5.2 and 5.8
Chapter 8: Cosmology - sections 8.1, 8.2, 8.3
Besides these basic topics, there has usually been some more material that has varied from year to year.
Lecture notes (scanned):

Chapter 0: Introduction to General Relativity
Chapter 1: Review of Special Relativity a, b, c, d, e, f, 23, 24, 25, 26, 27, 28, 29, h, i,
Chapter 2: Manifolds a, b, c, d
Chapter 3: Curvature a, b, c

Homework problem sets:

Homework 1
Homework 2
Homework 3
Homework 4
Homework 5

English-Finnish Dictionary
Gravity Probe B , finally the result

Gravitational wave detectors: LIGO VIRGO LISA

Last updated: February 20th, 2012.