HUOM! OPINTOJAKSOJEN TIETOJEN TÄYTTÄMISTÄ KOORDINOIVAT KOULUTUSSUUNNITTELIJAT HANNA-MARI PEURALA JA TIINA HASARI
1. Course title
General Relativity I
2. Course code
PAP348
Aikaisemmat leikkaavat opintojaksot 53736 Yleinen suhteellisuusteoria, 10 op ja PAP335 Yleinen suhteellisuusteoria, 10 op
3. Course status: optional
-Which degree programme is responsible for the course?
Master’s Programme in Particle Physics and Astrophysical Sciences
-Which module does the course belong to?
PAP3002 Advanced Studies in Particle Physics and Cosmology (optional for Study Track in Particle Physics and Cosmology)
TCM300 Advanced Studies in Theoretical and Computational Methods
-Is the course available to students from other degree programmes?
Yes
4. Course level (first-, second-, third-cycle/EQF levels 6, 7 and 8)
Master’s level, degree programmes in medicine, dentistry and veterinary medicine = secondcycle
degree/EQF level 7
Doctoral level = third-cycle (doctoral) degree/EQF level 8
-Does the course belong to basic, intermediate or advanced studies (cf. Government Decree
on University Degrees)?
Advanced studies
5. Recommended time/stage of studies for completion
This is an advanced course.
In terms of courses taught at the University of Helsinki, recommended prerequisites are Matemaattiset apuneuvot I ja II, Fysiikan matemaattiset menetelmät Ib, Fysiikan matemaattiset menetelmät IIa, Suhteellisuusteorian perusteet, Mekaniikka and Elektrodynamiikka. Fysiikan matemaattiset menetelmät III is helpful but not necessary.
6. Term/teaching period when the course will be offered
Lectured every spring term in period III.
7. Scope of the course in credits
5 cr
8. Teacher coordinating the course
Syksy Räsänen
9. Course learning outcomes
You will learn the physical and mathematical structure of the theory of general relativity.
You will learn how to do calculations in general relativity, including how to find the precession of the orbit of Mercury and the bending of light by the Sun.
10. Course completion methods
The course is offered in the form of contact teaching.
No attendance requirements.
The grade is based on the weekly exercises (1/3) and the exam (2/3). (Exception: for students who have taken the course before, the grade is based entirely on the exam.) You need about 45% of the maximum points to pass the course and about 25% to get the right to try to pass the course in a general exam. When retaking the exam, the exercise points are not counted towards the grade. It is only possible to retake a failed exam once without retaking the course. Not showing up for an exam without prior agreement counts as a failed attempt. If you pass the exam, you can try to raise your grade up to two times.
11. Prerequisites
-Description of the courses or modules that must be completed before taking this course or
what other prior learning is required
Mathematical methods, including non-Cartesian coordinate systems, coordinate transformations, linear algebra, vectors and tensors, Fourier transforms and partial differential equations. In terms of courses taught at the University of Helsinki, recommended prerequisites are Matemaattiset apuneuvot I ja II, Fysiikan matemaattiset menetelmät Ib, Fysiikan matemaattiset menetelmät IIa, Suhteellisuusteorian perusteet, Mekaniikka and Elektrodynamiikka. Fysiikan matemaattiset menetelmät III is helpful but not necessary.
Classical mechanics (including the variational principle), special relativity and electrodynamics.
12. Recommended optional studies
-What other courses are recommended to be taken in addition to this course?
-Which other courses support the further development of the competence provided by this
course?
- Cosmology I and II
- General relativity II
- Specialised courses in cosmology, such as Cosmological Perturbation Theory.
13. Course content
-Description of the course content
Chapter 1: review of symmetries in Newtonian mechanics, review of special relativity from the spacetime point of view, relativity principle in Newtonian mechanics and special relativity, electrodynamics in special relativity
Chapter 2: the equivalence principle, manifolds, tensors, the metric
Chapter 3: covariant derivative and connection, parallel transport, geodesics, curvature, Riemann tensor
Chapter 4: Einstein equation, Newtonian limit
Chapter 5: The Schwarzschild solution, precession of the perihelion of Mercury, bending of light by the Sun
14. Recommended and required literature
-What kind of literature and other materials are read during the course (reading list)?
-Which works are set reading and which are recommended as supplementary reading?
- The only required literature is the lecture notes.
- Recommended supplementary reading includes one or more of the following:
S.M. Carroll, Spacetime and Geometry (Addison Wesley 2004).
M. Nakahara: Geometry, Topology and Physics (IOP Publishing 1990)
S. Weinberg: Gravitation and Cosmology (Wiley 1972)
C.W. Misner K.S. Thorne, J.A. Wheeler: Gravitation (Freeman 1973)
R.M. Wald: General Relativity, (The University of Chicago Press 1984)
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).
J.B. Hartle: Gravity - An Introduction to Einstein's General Relativity (Addison Wesley 2003)
B. Schutz: Gravity from the Ground Up (Cambridge 2003)
15. Activities and teaching methods in support of learning
-See the competence map (https://flamma.helsinki.fi/content/res/pri/HY350274).
-Student activities
-Description of how the teacher’s activities are documented
16. Assessment practices and criteria, grading scale
-See the competence map (https://flamma.helsinki.fi/content/res/pri/HY350274).
-The assessment practices used are directly linked to the learning outcomes and teaching
methods of the course.
Course homepage https://www.mv.helsinki.fi/home/syrasane/gr/
17. Teaching language
English