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PAP335 General Relativity, 10 cr 
Code PAP335  Validity 01.01.2017 -
Name General Relativity  Abbreviation General Relativ 
Scope10 cr   
TypeAdvanced studies
TypeCourse   
  GradingGeneral scale 
  no
    Can be taken more than onceno
Unit Master's Programme in Particle Physics and Astrophysical Sciences 

Description
Target group 

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:
    1. 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.

 
Timing 

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.

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

 
Prerequisites 
  • 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.

 
Recommended optional studies 
  • Cosmology I and II
  • Specialised courses in cosmology, such as Cosmological Perturbation Theory.
 
Contents 
  • 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.
 
Study materials and literature 

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)
 


Current and future instruction
Functions Name Type cr Teacher Schedule
registration period has not begun General relativity  Lecture Course  10  Syksy Räsänen 
13.01.20 -24.02.20 mon 14.15-16.00
14.01.20 -25.02.20 tue 14.15-16.00
09.03.20 -06.04.20 mon 14.15-16.00
10.03.20 -07.04.20 tue 14.15-16.00
20.04.20 -27.04.20 mon 14.15-16.00
21.04.20 -28.04.20 tue 14.15-16.00

Future examinations
Functions Name Type cr Teacher Schedule
registration period has not begun General Relativity  General Examination  10  Syksy Räsänen 
17.01.20fri 12.00-16.00
registration period has not begun General Relativity  General Examination  10  Syksy Räsänen 
05.06.20fri 10.00-14.00
registration period has not begun General Relativity  General Examination  10  Syksy Räsänen 
14.08.20fri 10.00-14.00
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