PAP335 General Relativity (2020-2023)

1. Course title

Yleinen suhteellisuusteoria
Allmänna relativitetsteori
General Relativity

2. Course code

PAP335

Aikaisemmat leikkaavat opintojaksot 53736 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, covering both periods III and IV.

7. Scope of the course in credits

10 cr

8. Teacher coordinating the course

Syksy Räsänen

9. Course learning outcomes

-Description of the learning outcomes provided to students by the course
- See the competence map (https://flamma.helsinki.fi/content/res/pri/HY350274).

• 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 with black holes, linear perturbation theory, gravitational waves and a little bit also in cosmology.

10. Course completion methods

The course is offered in the form of contact teaching.
No attendance requirements.

The grade is based both on the weekly exercises (1/3) and on the two exams (1/3 and 1/3). (Exception: for students who have taken the course before, the grade is based entirely on the exams.) You need about 45% of the maximum points to pass the course (grade 1) and about 25% to get the right to try to pass the course in a department exam (this has to be done before the course is lectured again; registration for the department exam is done on WebOodi). When retaking the exam, the exercise points are not counted. It is only possible to retake the exam once without retaking the course. Not showing up for an exam without prior agreement counts as a failed attempt. The first and second exams cannot be retaken individually.

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.

• Differential geometry helps, but it is reviewed in the course, so previous knowledge is 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
• Specialised courses in cosmology, such as Cosmological Perturbation Theory.

13. Course content

-Description of the course content

• Review of special relativity.
• Basics of vector and tensor fields, as used in general relativity.
• Manifolds and differential geometry.
• Spacetime curvature and the Einstein equation.
• Black holes. Perturbation theory around Minkowski space. Gravitational waves. Symmetric spacetimes and the basics of the FRW metric and the Friedmann equations.

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