Timetable
Description
Master’s Programme in Particle Physics and Astrophysical Sciences is responsible for the course.
Modules where the course belong to:
 PAP300 Advanced Studies in Particle Physics and Astrophysical Sciences
Optional for: Study Track in Particle Physics and Cosmology
 TCM300 Advanced Studies in Theoretical and Computational Methods
The course is available to students from other degree programmes.

Mathematical methods, including nonCartesian 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.
 Cosmology I and II
 Specialised courses in cosmology, such as Cosmological Perturbation Theory.

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.
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.
Lectured every spring term, covering both periods III and IV.
 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.
The course is offered in the form of contact teaching.
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.
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)
The couse's webpage https://www.mv.helsinki.fi/home/syrasane/gr/