Course syllabus
Course-PM
FFM071 / FIM450 Gravitation and cosmology lp3 VT20 (7.5 hp)
Course is offered by the department of Physics
Contact details
- examiner: Bengt E.W. Nilsson, tfebn@chalmers.se, office Origo N6.109B, phone 0704-101283
- lecturer: Bengt E.W. Nilsson
- teachers: -
- supervisors:
- student representatives: presented during first week-Erik Andersson, Boel Brandström, Henric Ernbrink,
- Ludvig Svensson and Arvid Wenzel Wartenberg.
Course purpose
The purpose of the course is to give the student an understanding of
- why the gravitational force is naturally related to the geometry of spacetime
- the role of coordinate transformations and the equivalence principle
- the mathematical methods needed to make computations in general relativity
- the basic observations in gravity that supports Einstein's view, the bending of light etc
- black holes and gravitational waves
- the role of general relativity in cosmology and the big bang scenario
- why Einstein's theory of gravity is not the final answer
Schedule
Course literature
MAIN TEXT BOOK: (here referred to as SW, mandatory)
"Gravitation and Cosmology", Steven Weinberg (Wiley 1972)-available at Cremona
This book is very pedagogical and contains a lot of detailed calculations which makes it an excellent text book for a first course in general relativity. It is, however, a bit out of date in certain parts, e.g., those on gravitational waves and cosmology. The course will contain extended lecture notes on these two subjects to alleviate this problem.
plus (also mandatory)
1) Lecture notes- from the lectures (some handed out)
2) Collected problems - available as pdf-file via email
3) Some copies of recent research papers (only relevant for the examination if explicitly stated)- available from ArXiv or via email
ADDITIONAL TEXT BOOKS: (a bit more advanced than Weinberg's book)
1) "Modern General Relativity", Mike Guidry (Cambridge 2019)
2) "Spacetime and Geometry", Sean C. Carroll (Cambridge 2019)- parts available on ArXiv as hep-th/9712019
HISTORICAL TEXTS:
1) "The principle of relativity", collected papers by Einstein, Lorentz, Weyl and Minkowski (Dover1952).
2) "The meaning of relativity", A. Einstein (Chapman and Hall 1978) First printed by Methuen 1922.
Course design
The reading instructions for each lecture below defines the content of the course.
Note that some material covered in the lectures does not appear in the book by Weinberg (SW) while, at the same time, in the lectures we will not have time to discuss every single aspect of all the sections in SW that are included in the course.
All the 20 sessions (2 x 45 minutes) are lectures. There are thus no separate exercise classes but some lectures will contain problems presented to the students and time to contemplate how to solve them. The solutions (or hints) are then given on the black board.
A good strategy is therefore to go through each lecture immediately afterwards to make sure your understanding of the material discussed is under control and to check how it compares to the sections given below for that lecture. Should questions arise that you can't answer please discuss them with your fellow students or contact me. I will always be available on email and in my office when I am there.
SCHEDULE (date): All lectures in FL64
Lecture 1 (20/1): Introduction to Einstein's theory of gravity. Read the handed out lecture notes (contains a brief review of EM) and SW Chapter 1, Sections 2 and 3, Chapter 2, Sections 1 - 9, and Section 4.10.
Doc1-2020-Notes lecture 1-Intro to GR.pdf
Lecture 2 (22/1): Geometry, coordinates and the metric. Read handed out lecture notes and SW Chapter 1, Section 1.
Doc2-2020-Notes lecture 2-Coordinates and metrics.pdf
Doc3-2020-Home problems-set 1.pdf
Lecture 3 (27/1): The principle of equivalence. Read SW Chapter 3. Is there an error on page 80?
Doc4-2020-GPS and Relativity.pdf
Lecture 4 (29/1): Tensor analysis. Read SW Chapter 4, Sections 1 - 9.
Doc5-2020-Basic tensor analysis.pdf
Lecture 5 (29/1): Effects of gravity. Read SW Chapter 5, Sections 1 - 3.
Lecture 6 (3/2): Curvature. Read SW Chapter 6 (see the lectures for some simplified derivations).
7/2: Deadline (at noon sharp) for the first set of home problems.
Lecture 7 (10/2): Cont. from previous lecture.
10/2: Start-up meeting with the course representatives.
Doc6-2020-Home problems-set 2.pdf
Home problems (Hp) 6 - 10 from Doc6 are:
Hp6: problem 4.3.2, Hp7: problem 4.3.6, Hp8: problem 4.3.9,
Hp9.1: problem 4.4.1, Hp9.2: problem 4.4.3, Hp10: problem 4.4.5.
Doc7-2020-Notes lecture 3 - Equiv. principle.pdf
Doc8-2020-Notes lecture 4 -Tensors.pdf
Lecture 8 (12/2): Einstein's field equations. Read SW Chapter 7, Sections 1 and 4 - 6.
Lecture 9 (12/2): Cont. from previous lecture.
Lecture 10 (17/2): Classical tests of GR. Read SW Chapter 8. The subject in Section 8.8 is also discussed in the lecture on black holes.
17/2: Extra question session 14.00 - 16.00 in F-N6115.
Lecture 11 (19/2): Cont. from previous lecture.
Lecture 12 (19/2): Cont. from previous lecture.
24/2: Deadline (at noon sharp) for the second set of home problems.
24/2: Mid-course meeting with the course representatives.
Doc9-2020-Home problems-set 3.1.pdf
Home problems 11 - 13 from Doc9: can give 10 points each. Deadline: noon Friday 6/3.
11) 4.4.7 on AdS3, 12) 4.5.6 on (un)stable orbits, 13) 4.5.7 with Spiff on Buster.
(problems 14 and 15 later)
Lecture 13 (24/2): Gravitational waves. Read SW Chapter 10, Sections 1 - 5 and parts of Sections 6 - 9 (see lectures for details).
Doc10-2020-Abbott et al, Observations of GW.pdf
Lecture 14 (26/2): Cont. from previous lecture.
Lecture 15 (26/2): Cont. from previous lecture.
Doc12-2020-Observation of Gravitational Waves from a Binary Black Hole Merger « Einstein-Online.pdf
Doc13-2020-Notes lectures 13 - 15 - Grav waves.pdf
Lecture 16 (2/3): Symmetric spaces. Read SW Chapter 13 (see lecture for details).
Lecture 17 (4/3): Cosmology. Read SW Chapter14, Sections 1 - 3 together with Section 5.4, and Chapter 15, Section 1, plus handed out lectures notes.
Lecture 18 (4/3): Cont. from previous lecture.
Doc14-2020-Home problems-set 3.2.pdf
Home problems 14 and 15: see problem sheet in Doc14, deadline March 11 at noon.
Hp 14: problem sheet 4.6.2, Hp 15: problem sheet 4.7.2 (10 points each).
5/3: Doc15-2020-MSc-Notes lecture 17 and 18-Cosmology.pdf
5/3: Doc16-2020-Oral reading instructions .pdf
Lecture 19 (9/3): Black holes. Read Carroll (ArXiv hep-th/9712019) parts of Chapter 7 pages 164 - 192 (see lecture notes for details). The new material starts with the gravitational redshift discussion on page 180. Pages 164 - 180 contains a very nice account of things already covered in the course except for the Birkhoff's theorem and the corresponding derivation of the Schwarzschild solution!
9/3 at 14.00 - 16.00 in F-N6115: Extra question session
Lecture 20 (11/3): The Einstein-Hilbert action and why Einstein's theory of gravity cannot be the final story. Read SW Chapter 12, Sections 1 - 4.
11/3: Deadline (at noon sharp) for the third set of home problems.
13/3 at 13.15 (may change): Extra meeting. The corrected third set of home problems will be returned. You need 50% of the total number of points on all the home problems to sign up for the oral exam.
16 - 20/3: Oral exams. Detailed information on dates, how to sign up and what to read will be provided (via email) about two weeks before the examination week.
15/3: All orals exams will be done on Zoom. I will send you an email with a link a few minutes before your scheduled time for the oral. Just use the link to get connected to the session. Keep the text book (Weinberg) and your home problems close by if you need them.
Changes made since the last occasion
Some material on black holes have been replaced by an extended discussion on cosmology and the big bang scenario.
Learning objectives and syllabus
During the course the student is expected to acquire a basic understanding of the concepts and principles of general relativity and a working knowledge of the mathematics developed in the course. This means that the student should be able to discuss and explain the physical ideas behind and phenomena explained by Einstein's theory of gravity, general relativity, and in a skilful way use the relevant mathematical methods in problem-solving.
Learning objectives are to:
- understand Einstein's principle of equivalence.
- get an understanding and a working knowledge of the mathematical description of curved spaces and spacetimes including how to use tensor.
- understand how the presence of matter and energy affects the geometry of spacetime
- derive and understand the structure Einstein's equations and the basic steps for how to solve them in certain simple cases.
- describe how gravitational waves are generated, propagated and observed on Earth
- the structure and properties of black holes
- symmetric spaces and models of cosmology together with the equations governing the evolution of the universe and its properties at various time periods since the big bang
- be able to derive Einstein's equations from an action principle, and explain how this action principle can be used to couple the theory to other physical theories, such as electrodynamics.
- put Einstein's theory of gravity into the context of QFT and understand the basic arguments which indicate that this theory is incomplete and thus not the final story
Link to the syllabus on Studieportalen.
Examination form
The examination is divided into two mandatory parts (with grading weights given below):
1) A number of home problems (weight:40%)- these will appear in three sets with three different deadlines and 50% is required to do the oral.
2) An oral exam (weight:60%)- a 40 - 50 minutes long discussion mainly on concepts, how to derive certain equations and how solutions to them are obtained, relevant observations in GR etc, but also technical issues from the home problems might come up. The student must bring the corrected home problems to the oral. The student will NOT be asked to do calculations on the black board.
Course summary:
| Date | Details | Due |
|---|---|---|