Introduction to General Relativity

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Introduction to General Theory of Relativity. Fall 2015.

[ old home | old exams: problems-1, problems-2, problems-3 ]

NB:

Examination instructions:
1. Get the set of examination problems here or at your "digital examination" server.
2. You have to choose---at your own choice---and then solve four problems: one problem from Part-1, one from Part-2, one from Part-3 and one from Part-4.
3. If your årskortnummer ends with digits 0,5,7,8 you should in each Part choose a problem from (roughly) the first one-third (that is, if there are 12 problems in the Part you have to choose a problem from the problems with numbers 1,2,3,4).
4. If your årskortnummer ends with digits 1,2,9 you should in each Part choose a problem from the second one-third.
5. If your årskortnummer ends with digits 3,4,6 you should in each Part choose a problem from the last one-third.
6. If you don't have an årskortnummer, get your number from this list.
7. If you work in a group, you have to choose different problems as compared to your group-mates.
8. Provide sufficiently extensive answers. A criterion is that your fellow students must in principle be able to fully understand your answers.
9. At the end you may---if you wish---give me your self-evaluation (using the 7-point Danish system: -3,0,2,4,7,10,12) of your achievements in learning general relativity, including both the examination results and your work during the course. This is for statistics only and will not affect your grade.
10. Scanned handwriting is ok.
I have added a chapter about measuring small proper time- and length-intervals (measuring finite time- and length-intervals usually makes little sense in a time dependent metric space) should you need this for the examination exercises.
Check that you are in this examination list and record your number at the left column.

Schedule:

Lecture notes:

[ PDF; page-1.png page-2.png page-3.png page-4.png ] (25.06) Introduction. Special relativity.
[ PDF, page-1.png page-2.png page-3.png page-4.png ] (25.06) Einstein's principle of equivalence between gravitational and interital forces.
[ PDF; page-1.png page-2.png page-3.png page-4.png ] (25.06) Vectors in curvilinear coordinates. Covariant differentiation. Christoffel symbols.
[ PDF, page-1.png page-2.png page-3.png ] (25.06) Motion of free bodies in curved spaces. Geodesics.
[ PDF, page-1.png page-2.png page-3.png page-4.png page-5.png ] (25.06) Electrodynamics in gravitational fields. Lorentz force and Maxwell equations.
[ PDF, page-1.png page-2.png page-3.png ] (25.06) Action of matter in gravitational fields. Energy-momentum tensor of matter.
[ PDF, page-1.png page-2.png page-3.png page-4.png ] (25.06) Riemann curvature tensor; Hilbert-Einstein action of gravitation; Gravitational field equation (Einstein equation).
[ PDF, page-1.png page-2.png page-3.png ] (25.06) Newtonian limit of general relativity. Gravitational waves.
[ PDF, page-1.png page-2.png page-3.png ] (25.06) Schwarzschild solution. Motion in the Schwarzschild metric.
[ PDF, page-1.png page-2.png page-3.png ] (25.06) Classical tests: anomalous perihelion shift; bending of light; gravitational redshift.
[ PDF, page-1.png page-2.png ] (25.06) Radial fall in the Schwarzschild metric. Lemaitre coordinates. Event horizons. Black holes.
[ PDF, page-1.png page-2.png page-3.png page-4.png ] (25.06) Geomerty in a homogeneous and isotropic universe. Friedman equation.
[ PDF, page-1.png page-2.png page-3.png ] (25.06) Solutions to Friedman equation. Big Bang. Cosmological redshift. Hubble constant.
[ PDF, page-1.png ] (25.06) Proper time and length intervals in general relativity.

Lecturer:

Dmitri Fedorov

Literature:

A. Einstein, Relativity: The Special and General Theory [ps, PDF];
Gerard 't Hooft, Introduction to General Relativity [500kB PDF file], Rinton Press, Inc., Princeton NJ, ISBN 1-58949-000-2.
Warren Siegel, Fields, http://arxiv.org/abs/hep-th/9912205, (1215kb PDF file).

Links:

Old home, Wikipedia, MathWorld