Course PM

Problem Session Log
Homework Problems
Old Exams

Course Literature
Theory of Relativity
Course PM 2006

The course PM is also available as a PostScript or as a PDF file.

Course aim:
To help students recognize a black hole and avoid falling into one.

Previous knowledge corresponding to the tensor calculus part of 5A1305 Mathematical Methods in Physics and 2A1840 Electromagnetic Theory F.

Course content:

The course is divided into three parts:
  1. special relativity,
  2. differential geometry and
  3. general relativity.
The course consists of 14 lectures of 2 hours each. The first part of the course (special relativity) is treated in the first 7 lectures and the final 7 lectures are divided among the second (differential geometry) and third (general reltivity) parts. There will also be 10 problem sessions of 2 hours each. The course will be given in english if necessary.

Below is a listing of the course contents:
Special Relativity
  • Geometry of the Minkowski Space
  • Lorentz Transformations
  • Physical interpretations
    • Lorentz Contraction
    • Time Dilation
    • Relativistic Addition of Velocities
    • The invariance of the Speed of Light and the Michelson-Morley Experiment
    • The Relativistic Doppler Effect
  • The Proper Time and the Twin Paradox
  • Transformations of Velocities and Accelerations
  • Energy, Momentum, and Mass in Relativity Theory
  • Spinorial Representation of Lorentz Transformations
  • Lorentz Invariance of Maxwell's Equations
    • Physical Consequences of Lorentz Transformations
    • The Lorentz Force
    • The Energy-Momentum Tensor
Differential Geometry
  • Manifolds
  • Vector Fields and Tangent Vectors
  • Geodesics
    • Affine Connection and Christoffel Symbols
    • Parallel Transport
  • Torsion and Curvature
  • Metric and Pseudo-Metric
General Relativity
  • The Einstein Field Equations
  • The Newtonian Limit
  • The Schwarzschild Metric
  • Experimental Tests of General Relativity
    • The Gravitational Redshift
    • The Perihelion Precession of Mercury
    • The Bending of Light
    • Radar (Laser) Echo Delay
    • Black Holes, Binary Star Systems, and Stellar Evolution
  • Cosmological Models
    • The Large Scale Structure of the Universe
    • The Robertson-Walker Metric

Course literature and other recommended literature:

See the page Course Literature.


See the page Teachers.

Course homepage:

The course homepage can be found at: http://courses.physics.kth.se/5A1326/

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

Homework problems:

During the course, four non-compulsory homework problems will be handed out. For each set of homework problems passed by a student, one (1) bonus point is awarded at the course examinations during the academic year 2005-2006. Thus, a total of four (4) bonus points can be awarded.

Note! The solutions to the homework problems must be handwritten.

Even if the homework problems are non-compulsory, they are strongly recommended as the bonus points are often the difference between pass and fail on the final exam.

Course requirements:

One written exam (TEN1; 4 credits). The exam is a mixture of theory and problem solving assignments. The exam consists of six problems, each of which can give three (3) points, i.e., the maximum attainable score is 18 points, the bonus points from the homework problems are then added to this score. The only allowed aid for the examination is the collection of formulas at the end of the course compendium, copies of this will be available at the exam - you are not allowed to bring your own copy. The exam is graded with U, 3, 4, or 5. The exam results will be posted outside the student expedition.

Old exams can be downloaded from the course homepage.

Upcoming examinations:

  • Sat, March 11, 8:00-13:00, Rooms FB53-55
  • Mon, June 5, 14:00-19:00, Room FB52
The times are preliminary, check the KTH Schedule for updates.

Examiners: Jouko Mickelsson och Håkan Snellman.


See the KTH Schedule.

Last updated: Jan 2, 2006