FY3452 Gravitation and Cosmology

Våren 2010

  • Lecturer: Michael Kachelrieß, office: E5-149

  • !!! Room Change: Dato: torsdag, 18.02.2010 --> R20 !!!

  • Description:
    The course gives a general introduction to classical field theory, special and general relativity including applications, in particular cosmology.
    The course is aimed at physics students in the 3.nd/4.th year.
    Lectures: Monday 10.15-12.00 R73, starting from 11.1.
    Lectures: Thursday 10.15-12.00 R10 (=D5-171)
    Exercises are not mandatory, but an integral part of the course.

  • Recommended books:
    Books covering the "pensum":
    1. J. B. Hartle. Gravity: An Introduction to Einstein's General Relativity (Benjamin Cummings), ISBN-10: 0805386629.
    2. Lecture notes "Klassisk feltteori" by Jan Myrheim (can be bought at the 'espedisjon' for NOK 100).
    Additional lecture notes will be distributed, should we make digressions not covered by 1. and 2.

    Alternative literature (useful for a deeper math. background) from the net:
    1. Carroll, Sean M.: Lecture Notes on General Relativity. arXiv:gr-qc/9712019 v1 3 Dec 1997.
    2. Waner, Stefan: Introduction to Differential Geometry and General Relativity.

    Check out also the library for books you like:     For instance, look for

  • Reference group:
    Erik Bakken: erikmaki@stud.ntnu.no
    Aasmund Ervik: asmunder@stud.ntnu.no


  • Program: (numbers refer to the corresponding chapters in Hartle's book or Myrheim's compendium)
    Week 2: Special relativity [H4, H5] notes.
    Week 3: Classical mechanics. Lagrangian and Hamiltonian formulation [M4]
    Week 4: Classical field theory [M6-M8]
    Week 5: Differential geometry [H7, H8, H20]
    Week 6: Schwarzschild solution [H9] notes.
    Week 7: Gravitational lensing, black holes [H10, H11.1, H12, H15]
    Week 8: Black holes
    Week 9: Exercise week, no lectures.
    Week 10: Black holes notes.
    Week 11: Curvature, Einstein equations[H21, H22]
    Week 12: Linearized gravity, gravitational waves [H16, H21, H23] notes.
    Week 13: Easter holidays
    Week 14: (only Thu.) Cosmology: FRW models [H18] notes.
    Week 15: FRW models [H18]
    Week 16: Inflation, structure formation
    Week 17: (only Mon.) Repetition & open questions


  • Exercises and solutions:
    Week 3: exercises and solutions.
    Week 4: exercises and
    Week 5: exercises and solution 7.14.
    Week 6: exercises and .
    Week 7: exercises and .
    Week 8: exercises and extra exercises
    Week 15: exercises and some solutions

  • Solutions to selected exercises from Hartle's book:
    chapter 4.
    chapter 5.
    chapter 7.
    chapter 8.
    chapter 9.
    chapter 12.



  • E. Wright's cosmology calculator: here.

  • Pensum: The pensum for the exam is defined by the content of the lectures, not by the book of Hartle. Thus you can skip Ch. 14, 23 and 24, but you should add some classcial mechanics/field theory. To make life easier, you can also skip week 16.

  • Exam 2010 you can dinf the exam with solutions here.

  • Exam 2009 can be downloaded here, the exam with solutions here. For the sign of the energy-momentun tensor see below.

  • Sign conventions There exist various sign conventions for the metric, the Ricci and the Riemann tensor, and therefore also in Lagrangians, field equations, etc. Mixing different conventions, two sign errors crept in the derivation of the field equations and dynamical energy-momentum tensor: in the definition of the dynamical energy-momentum tensor a minus sign should be added, as well as a minus sign in the "kinetic term" of the fields.

  • Some original works (on the level of these lectures)
    J. Bekenstein: Black holes and entropy.
    J. Bekenstein: Black holes and information theory.
    A. Friedmann: Über die Krümmung des Raumes.

    Last up-date: 5.5.2010