FYTN08, General Relativity, 7.5 ECTS
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
Introduction MeetingMonday 20 March 2017, 10.15, Andromeda, Astronomy building. Lectures on Monday, Wednesday and Friday 10.15-12.00 in the same room (with some exceptions). The preliminary schedule can be found below
Spring 2017 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
The exercises in spring 2017 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.
ExaminationThere 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 9/5, Wednesday 10/5 and Thursday 11/5 8.15-12.00
(who presents what decided at the latest Friday 28 April, wishes to be given at the lecture Wednesday 26 April)
Schedule spring 2017 (with presentations, times and dates), continuously updated.
- Take home exam: Wednesday 17/5-Wednesday 24/5 with presentation of the results and solutions Friday 26/5 or Monday 29/5.
- Oral exam: Monday 29/5, Tuesday 30/5, Wednesday 31/5, Thursday 1/6, Friday 2/6 normally in my office
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.
Week Date Room Content w12 Monday 20/3 Andromeda Introductory meeting and special relativity Wednesday 22/3 Andromeda Special relativity: geometrical view and vector analysis Friday 24/3 Andromeda Tensor analysis in special relativity w13 Monday 27/3 Andromeda Equivalence principle and preparing for curvature Wednesday 29/3 HUB Preparing for curvature, Curved manifolds Friday 31/3 Andromeda Exercises and Questions w14 Monday 3/4 HUB Curved manifolds Wednesday 5/4 HUB Curved Manifolds, Energy momentum tensor
Optional: geodesic equation from shortest distance
Friday 7/4 Andromeda Energy-Momentum Tensor, Physics in curved space times w15 Monday 10/4 Andromeda Exercises and questions w16 Wednesday 19/4 Andromeda Einstein Field Equations, Weak field equations Friday 21/4 Andromeda Spherically symmetric metrics w17 Monday 24/4 Andromeda Spherically symmetric solutions and stars Wednesday 26/4 Andromeda Orbits, perihelion shift and deflection of light
A java applet to play with orbits
An alternative solution to the deflection of light equation
Friday 28/4 Andromeda Exercises and Questions w18 Wednesday 3/5 HUB Black Holes Friday 5/5 HUB Hawking Radiation, Gravitational Radiation w19 Monday 8/5 Andromeda Gravitational radiation, Recent discovery Tuesday 9/5 Andromeda Presentations Wednesday 10/5 Andromeda Presentations Thursday 11/5 Andromeda Presentations Friday 12/5 Andromeda Exercises and Questions w20 Monday 15/5 Andromeda Cosmology Wednesday 17/5 Andromeda Exercises and Questions Friday 19/5 Andromeda Cosmology: advanced topics, Presentation w21-22 Exam: Schedule see above
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.
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.
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 as
Other 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.
Contact, phone 046-2220447
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The results from earlier years:
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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.
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
- 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: