// Aarhus University / Physics / Subatomic Physics / Nuclear Theory
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Introduction to General Theory of Relativity. Fall 2009.
- NB:
- Examination: Wednesday, Oct 28, 09:15-12:00, aud.
1531-119 (aud. D2 in mathematics);
- Deadline for exercises: Wednesday, Oct 21 (put it in my mailbox in
the post-room next to "information" in physics);
- Consultation meeting will be on Monday, Oct 26, 13:15-15:00, aud.
1520-216.
- Schedule:
- Lectures: Tuesday, 12:15, 520-616; Thursday, 10:15, 520-616
- Seminars: Monday, 08:15, 520-616
- Lecture notes:
-
-
[
pdf,
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(25.06)
Introduction. Einstein's equivalence principle.
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pdf,
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(25.06)
Special relativity: do it yourself on week 36.
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pdf,
png-1,
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(25.06)
Curved spaces. Vectors in curvilinear coordinates. Covariant
differentiation.
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[
pdf,
png-1,
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(25.06)
Motion of free bodies in curvilinear coordinates. Geodesics.
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[
pdf,
png-1,
png-2
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(25.06)
Action. Variational (least action) principle.
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pdf,
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(25.06)
Action of matter in gravitational fields. Energy-momentum tensor.
Obligatory exercises: energy-momentum tensor of scalar and vector
fields.
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[
pdf,
png-1,
png-2
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(25.06)
Riemann curvature tensor;
Hilbert-Einstein action of gravitation;
Gravitational field equation (Einstein equation). Obligatory exercise:
Riemann tensor on a surface of a sphere.
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[
pdf,
png-1,
png-2
] (25.06)
Newtonian limit of general relativity.
Gravitational waves. Obligatory exercise: clock rates in a
gravitational potential.
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[
pdf,
png-1,
png-2
] (25.06)
Schwarzschild solution. Motion in the Schwarzschild metric. Obligatory
exercises: Newtonian limit; Classical trajectories of planets.
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[
pdf,
png-1,
png-2
] (25.06)
Classical tests:
anomalous perihelion shift;
bending of light;
gravitational redshift. Obligatory exercise: Kepler's law of
planetary motion.
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[
pdf,
png-1,
png-2
] (25.06)
Radial fall in the Schwarzschild metric. Lemaitre
coordinates. Event horizons. Black holes.
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[
pdf,
png-1,
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Homogeneous and isotropic universe.
Friedman
metric. Friedman
equation. Obligatory exercise: temporal development of a flat
Friedman universe.
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[
pdf,
png-1,
png-2
] (25.06)
Solutions to Friedman equation. Cosmological
redshift. Hubble
constant.
- Lecturer:
- Dmitri Fedorov
- Literature:
-
-
Pensum:
ps,
pdf, png,
html
(25.06)
-
GTR FAQ:
ps,
pdf, png,
html
(25.06)
-
Gerard 't Hooft, Introduction to General Relativity,
(500K
PostScript 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
Copyleft
©
2005-2007 D.V.Fedorov
(fedorov @ phys au dk)
