FYTN08, General Relativity, 7.5 ECTS
Spring 2018
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.thep.lu.se/english/education/courses/general_relativity/.
Introduction Meeting
Tuesday 20 March 2018, 9.15, Lundmarksalen, Astronomy building (Note the time!). Lectures on Monday, Wednesday and Friday 10.15-12.00 in Andromeda, Astronomy building (with some exceptions). The preliminary schedule can be found belowExercises
Spring 2018 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, Comment about the last part of 8.19, solution of the thinking about problem - Exercises set 4 solutions set 4
- Exercises set 5 solutions set 5
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: Thursday 3/5, Tuesday 8/5, Wednesday 9/5 8.15-12.00
(who presents what decided at the latest Friday 27 April, wishes to be given at the lecture Wednesday 25 April)
Schedule spring 2018 (with presentations, times and dates), continuously updated. - Take home exam: Wednesday 16/5-Wednesday 23/5 with presentation of the results and solutions Friday 25/5 or Monday 28/5.
- Oral exam: Monday 28/5, Tuesday 29/5, Wednesday 30/5, Thursday 31/5, Friday 1/6 normally in my office
- Reexam will take place in the second half of August 2018. Contact me in good time if you want to do this, before the 10th of August. Planned schedule: hand out of take home exam: Wednesday 15 August, due Wednesday 22 August 12.00 (noon) corrected exams ready at the latest Monday 27 August (but probably on Friday 24) with oral exam opportunities to be discussed then, these will in the week 27-31 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 still possible.
Week Date Room Content w12 Wednesday 21/3 Andromeda Special relativity Friday 23/3 Andromeda Special relativity: geometrical view and vector analysis w13 Monday 26/3 Andromeda Tensor analysis in special relativity Wednesday 28/3 Andromeda Exercises and Questions w14 Wednesday 4/4 Andromeda Equivalence principle and preparing for curvature Friday 6/4 Andromeda Preparing for curvature, Curved manifolds w15 Monday 9/4 Andromeda Curved manifolds Wednesday 11/4 Andromeda Curved Manifolds, Energy momentum tensor
Optional: geodesic equation from shortest distanceFriday 13/4 Andromeda Exercises and Questions w16 Monday 16/4 Andromeda Energy-Momentum Tensor, Physics in curved space times Wednesday 18/4 Andromeda Einstein Field Equations, Weak field equations Friday 20/4 Andromeda Spherically symmetric metrics w17 Monday 23/4 Andromeda Spherically symmetric solutions and stars Wednesday 25/4 Andromeda Orbits, perihelion shift and deflection of light
A java applet to play with orbits
An alternative solution to the deflection of light equationFriday 27/4 Andromeda Exercises and Questions w18 Wednesday 2/5 Andromeda Black Holes Thursday 3/5 Andromeda Presentations Friday 4/5 Andromeda Hawking Radiation, Gravitational Radiation w19 Monday 7/5 Andromeda Gravitational radiation, Recent discovery Tuesday 8/5 Andromeda Presentations Wednesday 9/5 Andromeda Presentations Friday 11/5 Andromeda Exercises and Questions w20 Monday 14/5 Andromeda Cosmology Wednesday 16/5 Andromeda Exercises and Questions Friday 18/5 Andromeda Cosmology: advanced topics, Presentation w21-22 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.
- Warwick general relativity course lecture notes (similar level)
- 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
To help us improve our courses we want you to complete a course evaluation after the examination.
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
- 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