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Relativity Theory
Course PM 2010




Course aim:

After completion of the course you should be able to:
  • Use tensor notation in relativity theory.
  • Apply the concepts of length contraction and time dilation as well as use Lorentz transformations.
  • Solve simple kinematical problems.
  • Analyze Maxwell's equations and use their relativistic invariance.
  • Compute basic quantities in differential geometry.
  • Analyze Einstein's field equations as well as know and use some important solutions to these.
  • Report some experimental tests of general relativity.
  • Have knowledge about cosmological models.
  • Explain the physical interpretations and implications of SR and GR.


Prerequisites: Vector analysis; theory of electromagnetism; mathematical methods in physics.


Course content:

The course is divided into three parts:
  1. special relativity,
  2. tensors and curved spaces,
  3. general relativity.
The course consists of 15 lectures of 2 hours each. There will also be 15 problem sessions of 2 hours each. The course will be given in English.

Below is a listing of the course contents:


Special Relativity (SR)
  • Coordinate symmetries
  • Newtonian physics and Galilean symmetry
  • Electrodynamics and Lorentz symmetry
  • Physical implications of Lorentz transformations (length contraction, time dilation, Doppler effect, twin paradox etc.)
  • Relativistic momentum and energy-momentum tensor
  • Geometry of the Minkowski space
  • Tensors in SR

Tensors and curved spaces
  • Tensors in SR
  • Curved surfaces  in R³
  • Introduction to Riemannian geometry (Levi-Civita connection, Christoffel symbols, tensors, curvature etc.)
General Relativity (GR)
  • Newton's theory of gravitation
  • The principle of equivalence
  • Physical implications of the EP (gravitational redshift and time dilation, light ray deflection, curved spacetime)
  • GR equation of motion (geodesic equation) and implications (Newtonian limit, gravitational redshift etc.)
  • Curvature of spacetime and tidal forces
  • Schwarzschild spacetime and it physical implications (perihelion precession, gravitational lensing, black holes)
  • Introduction of cosmology  (experimental facts and models based on GR: Robertson-Walker model and Friedmann equations)
  • Einstein field equation and implications (Newtonian limit, description of a few important solutions, gravitational waves)


Course literature and other recommended literature:

See the page Course Literature.


Teachers:

See the page Teachers.

Course plan:

See the page Course Plan.

Course homepage:

The homepage will be updated throughout the course. A problem session log of what has been treated during the sessions will be available.


Midterm tests (KS):

During the course, three midterm tests, 1 hour each, will be given. There will be two assignments handed out, from which you choose one to solve. Any litterature mentioned on the homepage are allowed to bring. A maximum of four bonus points can be achieved by doing these tests, according to: more than 75% gives 4 p, more than 50% gives 3p more than 25% gives 2p and more than 0% gives 1p. The bonus points are only valid during the academic year 2010-2011.


Course requirements:

One written exam (TEN1; 7.5 credits). The exam is a mixture of theory and problem solving assignments. The only allowed aid for the examination is a collection of formulas available here:   , copies of this will be available at the exam - you are not allowed to bring your own copy. The exam is graded with A, B, C, D, E, F, Fx.

The exam will consist on two parts: Part I will contain standard problems and questions, similar to exercise and homework which you will be given during the course, to check that you reached the minimum level to pass the course, whereas Part II will contain more difficult problems. Each part consists of three problems and/or questions which can give six (6) points maximum each, and the bonus points from the midterm tests will be added to the points from Part I but the maximum points for Part I which you can reach is 19, i.e. the total number of points in the exam will be evaluated as

#points=min(19,#points for Part I+Bonus points) + #points for Part II

A "Fx", "E", "D", "C", "B" and "A" are guaranteed for  15, 18, 22, 26, 30 and 34 points, respectively (we might adjust this to lower point limits, depending on the difficulty of the exam).


Schedule:


See the page Schedule.
Last updated: Jan 18, 2010