Gravitation and Cosmology, Master course, 5p, Lp II, 2003

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Course codes: CTH:FFM 071, and GU:FY0320
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Lecturer:Bengt EW Nilsson, tel 772 3160, Origo 6104C,
Exercise classes:Pär Arvidsson, tel 772 3685, Origo 6107B,
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Literature:Steven Weinberg, "Gravitation and Cosmology
- Principles and Applications of the General Theory of Relativity",
John Wiley & sons, 1972.
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Schedule: Tuesday 13.15-15.00 in FL62, Thursday 08.30-12.00 in FL64,
Friday 13.15-15 in FL62
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Gravitation and Cosmology is a course whose purpose it to provide
a basic understanding of the foundations of general relativity, Einstein's
theory of gravitation. The subject is rather demanding conceptually
but at the same time extremely rewarding. The course provides a detailed
explanation of the mathematical methods used, in particular tensor
calculus, and relies on a set of logical steps leading
from the observations behind the equivalence principle all the way to
Einstein's equations. The course discusses several different experimental
tests of the theory and ends with applications to cosmology.
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Examination: The final exam is through a home exam handed out in
the middle of the course. The time limit for solving the problems
has been set to March 1, 2004 by a student decision. The oral exam should
scheduled for some time during the month of March, 2004.
There are on the exam sheet 12 problems with a total of 25 points.
CTH:
You need 10 p for mark 3 and 15 p for mark 4. To obtain the mark 5
one needs in addition to pass an oral examination
after the home exam has been handed in.
GU:
You need 10 p to pass, i.e. for mark G. For VG you need in addition to
pass an oral examination.
PhD:
You need at least 15 p plus passing an oral examination.
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Background requirements: There are no formal background requirements
for this course but some familiarity with special relativity is very useful.
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Lectures, exercise classes and content:
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1ST WEEK: Special relativity (week 44)

Lecture 1: Tuesday October 28, 13.15-15.00
Introduction, Chap 1, p.1-23, some additional examples of two-dimensional
metrics are presented
Lecture 2&3: Thursday October 30, 08.30-12.00
Special relativity, Chap 2, p. 25-52, rel. hydrodynamics only needed
later in the course. This chapter provides a recapitulation of useful
results in spec. relativity. The new and important aspect is the
use of tensor methods which will be extremely useful in the rest of
the course.
Lecture 4: Friday October 31, 13.15-15.00
cont. Special relativity.

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2ND WEEK: The equivalence principle (week 45)
For updated information see Table V in Tests of the Equivalence Principle
and links 'Info'->'Testing Equivalence' in STEP
Exercise class 1: Tuesday November 4, 13.15-15.00
Special relativity
Lecture 5&6: Thursday November 6, 08.30-12.00
The equivalence principle, Chap 3, p. 67-88, sect 3.7 on 'Relativity and
anisotropy of inertia' is less important.
Lecture 7: Friday November 7, 13.15-15.00
Tensor analysis, Chap 4.1-4.7 p. 91-108 and 4.9-4.10, p. 110-113.
Note that these sections, and in particular 4.6, are crucial for a proper
understanding of the rest of the material in this course.

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3RD WEEK: Effects of gravitation, curvature(week 46)

Exercise class 2: Tuesday November 11, 13.15-15.00
Tensor analysis
Lecture 8&9: Thursday November 13 , 08.30-12.00
Effects of gravitation, Chap 5, plus energy-momentum and hydrodynamics
from Chap 2
Curvature, Chap 6.1-6.8, p. 131-147, we use sect 6.5 to introduce the curvature
tensor and you can then read sect 6.1 for a more standard proof of its
transformation properties.
Lecture 10: Friday November 14, 13.15-15.00
cont. Curvature, Chap 6.
Sections 6.9 and 6.10 are not included in the
course but give some additional insight. Note the first paragraph of
sect 6.9 and the comments on the unimportance of geometry in high energy
physics. This is not so today!!

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4TH WEEK: Einstein's equations and classic tests (week 47)

Exercise class 3: Tuesday November 18, 13.15-15.00
Curvature and geodesics, Chap 6
Lecture 11&12: Thursday November 20, 08.30-12.00
Einstein's field equations, Chap 7.1 p.151-155, Chap 7.4-7.6, p. 161-171.
Sect 7.3 on the Brans-Dicke scalar field is not in the course but contains
interesting aspects: variable Newton's 'constant'. Scalar fields are
generic in string theory.
Lecture 13: Friday November 21, 13.15-15.00
Classic tests of Einstein's theory, Chap 8.1-8.3, p.175-185.
For a comprehensive review of GR tests see Confronting GR with experiments;
the first 13 pages are nice reading which give a hint of the present situation.
Our limited knowledge of the validity of the inverse-square law
and new (note the date of the article) experimental results are discussed in
Sub-millimeter tests of the inverse square-law: search for extra dimensions
See also (three first items) Tests of GR
and the nice ones on Frame dragging
and Frame dragging black holes
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5TH WEEK: Gravitational radiation and gravitons. Stellar collapse (week 48)

Lecture 14: Tuesday November 25, 13.15-15.00
Gravitational radiation, Chap 10.1-10.3, p. 251-260.
Comments on the Quantum theory of gravitation, sect 10.8.
See Gravitational radiation and the links to experiments,
LIGO etc, at the end. You may also check out Binary pulsars
and their discovery by Taylor and Hulse
The Nobel prize
Exercise class 4&5: Thursday November 27, 08.30-12.00
The Schwarzschild metric: sect 8.4-8.8, p 185-208.
Lecture 15: Friday November 28, 13.15-15.00
Stellar equilibrium and collapse, sects. 11.1-11.2, p. 297-308.
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6TH WEEK: Stellar collapse. The Einstein-Hilbert action(week 49)

Lecture 16: Tuesday December 2, 13.15-15.00
Time dependent stellar collapse: sects. 11.7-11.9
Exercise class 6&7: Thursday December 4, 08.30-12.00
Sects. 11.1- 11.4.
Lecture 17: Friday December 5, 13.15-15.00
The action principle, and the vierbein (tetrad): Chap 12.
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7TH WEEK: Symmetric spaces. Cosmology (week 50)
Check out Why is the universe accelerating
and Testing the cosmological constant as a candidate for dark energy
Lecture 18: Tuesday December 9, 13.15-15.00
Symmetric spaces: Chap 13
Lecture 19&20: Thursday December 11, 08.30-12.00
Cosmography: Sects. 14.1-14.3, and
cosmology: Sects. 15.1-15.3
Exercise class 8: Friday December 12, 13.15-15.00
Symmetric spaces, cosmography and cosmology
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8TH WEEK: Examination week of period II.