FYTN08, General Relativity, 7.5 ECTS
Spring 2019
Schedule, literature, etc.
This page can be found at http://home.thep.lu.se/~bijnens/fytn08.
The official home page for the course is at
http://www.atp.lu.se/english/education/courses/general_relativity/.
Introduction Meeting
Monday 25 March 2019, 10.15, Andromeda, Astronomy building. Lectures on Monday, Wednesday and Friday 10.15-12.00 in Andromeda, Astronomy building. The preliminary schedule can be found belowExercises
Spring 2019 exercises
- Exercises set 1 solutions set 1
- Exercises set 2 solutions set 2
- Exercises set 3
The effect calculated in Ex. 8.19 has been confirmed with high precision see http://einstein.stanford.edu/
solutions set 3, solution of the thinking about problem - Exercises set 4 solutions set 4
- Exercises set 5 solutions set 5
The exercises in spring 2019 are taken care of by
Physics and Mathematics required for this course
The amount of preknowledge required and how mathematical the course is (or should be) is discussed here.
Note that this is a master level theoretical physics course and the difficulty level is adjusted to that. It can be taken by bachelor students in their third year but tends to be rather hard at that level.
Examination
There are three parts:- Written take home exam
- Oral exam to test understanding with a list of typical questions and which parts of the book are not included
- Oral presentation of a special topic with a list of possible topics and references and hints/comments about the presentations.
- Presentations: Tuesday 7/5, Wednesday 8/5 and Thursday 9/5 8.15-12.00
(who presents what decided at the latest Monday 29 April, wishes to be given at the lecture Wednesday 24 April).
Schedule spring 2019 (with presentations, times and dates), continuously updated Note the starting time. - Take home exam (preliminary, might shift by a few days): Tuesday 21/5-Tuesday 28/5 with presentation of the results and solutions Wednesday 29/5 or Friday 31.
- Oral exam: , Friday 31/5, Monday 3/6, Tuesday 4/6, Wednesday 5/6, normally in my office
- Reexam will take place in the second half of August 2019. Contact me in good time if you want to do this, before the 15th of August. Planned schedule: hand out of take home exam: Monday 19 August, due Monday 26 August 12.00 (noon) corrected exams ready at the latest Wednesday 28 August (but probably on Tuesday 26) with oral exam opportunities to be discussed then, these will in the period 28-30 August.
Schedule and course contents
The lectures are Monday, Wednesday and Friday, 10.15-12.00, Andromeda, Astronomy building physics unless otherwise noted below. Links are to supplementary information. wx means week x in the Swedish week counting. Note that there will be lectures also after the exercises if they do not take the two hours. Small changes possible.
Week Date Room Content w13 Monday 25/3 Andromeda Introductory meeting and Special relativity Wednesday 27/3 Andromeda Special relativity: geometrical view and vector analysis Friday 29/3 Andromeda Tensor analysis in special relativity w14 Monday 1/4 Andromeda Equivalence principle and preparing for curvature Wednesday 3/4 Andromeda Preparing for curvature, Curved manifolds Friday 5/4 Andromeda Exercises and Questions w15 Monday 8/4 Andromeda Curved manifolds; derivation Riemann tensor Wednesday 10/4 Andromeda Curved Manifolds, Energy momentum tensor
Optional: geodesic equation from shortest distanceFriday 12/4 Andromeda Exercises and Questions w16 Monday 15/4 Andromeda Energy-Momentum Tensor, Physics in curved space times Wednesday 17/4 Andromeda Einstein Field Equations, Weak field equations w17 Wednesday 24/4 Andromeda Spherically symmetric metrics Friday 26/4 Andromeda Exercises and Questions w18 Monday 29/4 Andromeda Spherically symmetric solutions and stars Friday 3/5 Andromeda Orbits, perihelion shift and deflection of light
A java applet to play with orbits
An alternative solution to the deflection of light equationw19 Monday 6/5 Andromeda Black Holes Tuesday 7/5 Andromeda Presentations Wednesday 8/5 Andromeda Presentations Thursday 9/5 Andromeda Presentations Friday 10/5 Andromeda Hawking Radiation, Gravitational Radiation w20 Monday 13/5 Andromeda Gravitational radiation, Recent discovery Wednesday 15/5 Andromeda Exercises and Questions Friday 17/5 Andromeda Cosmology w21 Monday 20/5 Andromeda Exercises and Questions w22 Monday 27/5 Andromeda Cosmology: advanced topics, Presentation w22-23 Exam: Schedule see above Literature
The course book is: B.F. Schutz, A first course in general relativity, Second edition, Cambridge University Press, 2009, ISBN 978-0-521-88705-2. Some extra notes will be handed out for advanced topics. Note Second edition. Misprints for the first printing (pre 2011) of the second edition. Some misprints in second printing
A book covering essentially the same topics but with a more American style (boxes, different tracks, more storylike in places etc.) which is a recommended second read if you have difficulties with some topics in the course book is Thomas A. Moore, A General Relativity Workbook, University Science Books, 2013, ISBN 978-1-891389-82-5. There are unfortunately some differences in notation with the course book.
Possibly useful extra literature
There are very many books on general relativity. Below is a selection that I have found useful and/or interesting. Note the final part with books suggested as useful by other students (which I did not check out myself but clearly somone has found helpful)
Somewhat higher level:
- Sean Carroll, Spacetime and Geometry: An Introduction to General Relativity , Addison-Wesley, 2004, ISBN 0-8053-8732-3.
- Sean Carrol: Lecture notes on general relativity, arXiv:gr-qc/9712019
- James B. Hartle, Gravity: An Introduction to Einstein's General Relativity, Addison Wesley, 2002, ISBN 0-8053-8662-9.
- M.P. Hobson, G.P. Efstathiou and A.N. Lasenby, General relativity: an introduction for physicists, Cambridge University Press, 2006
- A. Zee, Einstein Gravity in a nutshell, Princeton University Press, 2013. This book uses the lagrangian formalism throughout, if you know this then a useful complement for those who want to know more and it goes on to a number of very advanced topics.
- John Dirk Walecka, Introduction to General Relativity, World Scientific, 2007
- Benjamin Crowell, General Relativity, http://www.lightandmatter.com/genrel/
- Bernard Schutz, Gravity from the Ground Up : An Introductory Guide to Gravity and General Relativity, Cambridge University Press, 2003, ISBN 0-5214-5506-5.
- Edwin F. Taylor and John Archibald Wheeler, Exploring Black Holes: Introduction to General Relativity, Addison Wesley, 2000, ISBN 0-2013-8423-X.
- Charles W. Misner, Kip S. Thorne, and John A. Wheeler, Gravitation, W. H. Freeman & Company, 1973
- Steven Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons, 1972
- Kevin Brown, Reflections on Relativity, MathPages, 2010, Exists also online http://mathpages.com/rr/rrtoc.htm
- "general relativity" will give you much more than you want
- "General Relativity by Leonard Susskind" Both lower level and higher level lectures exist.
- This channel is from The WE-Heraeus International Winter School on Gravity and Light
- Matthias Blau, University of Berne 900+ pages, has both good introductory and more advanced parts (but uses Lagrangians for some parts)
- Foster and Nightingale, A Short Course in General Relativity, Springer, 2006 (accessible online at Lund University)
Solutions to the exercises
Use these intelligently, i.e. first do a proper attempt to solve the problem yourself.
Solutions to a number of the exercises can be found in the appendix of the first edition of the book. A similar set of solutions for the second edition is accessible via Schutz's homepage asOther resources for the exercises:
There is a book that has the solution to about half the problems in the course book and a large number of additional problems as well. This is
Robert B. Scott, A Student's Manual for "A first course in general relativity,", Cambridge University Press, 2016, ISBN 978-1-107-63857-0.
More info via Robert Scott's notes for self study
- Solutions to Problems in General Relativity (for the first edition)
- There are many more sites with solutions, but be careful not everything on the web is correct.
Lecturer
Johan BijnensContact
, phone 046-2220447Course evaluation
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The results from earlier years:Academic honesty, gender equality and equal opportunity
Academic honesty, gender equality and equal opportunity for all are important for us. Specific guidelines and information about whom to talk to are in the department's guidelines.
Links
The wikipedia link collection for General Relativity might be useful.
An overview of cosmology and related results is the Universe from the WMAP collaboration.
Some others I found nice are:
- About black holes
- Film on gravitational waves
- The General Relativity Tutorial
- http://www.einstein-online.info/elementary.html
- Very basic relativity
- Physics of the universe
- Recent Nobel prizes in Physics related to things in this course, this page contains also low-level explanations:
Research links: some representative examples are:
- Professional preprint server
- Relativity bookmarks
- LIGO The US gravitational wave observatory
- Living Reviews in Relativity A series of review articles on various subjects, advanced but in overview understandable with the knowledge of the course