Classes |
TuTh 2:40-4:00, 1308 BPS. |
Instructor |
Mr.
Ed Loh, 3260 BPS, 884-5612, Loh@msu.edu |
Office
hours |
TuTh, 12:00-1:00, 3260 BPS, or as scheduled. |
Textbook |
Gravity, J. B. Hartle, Addison-Wesley, 2003. Errata:
http://web.physics.ucsb.edu/~gravitybook/Err-all.pdf |
Other
books |
Gravitation &
Cosmology,
S. Weinberg, 1972 Principles of Physical
Cosmology,
P. J. Peebles, 1993. Gravitation & Spacetime, H Ohanian & R. Ruffini, 1994. Cosmology, S. Weinberg, 2008. Subtle is the Lord, A. Pais,
1982. |
Web |
Dates |
Topic |
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Elementary gravity |
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Jan |
Introduction, lessons of
special theory that apply to gravity, Minkowski
metric, Schwarzschild metric |
§1-5 |
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Gravitational redshift
(Pound-Rebka). Shapiro effect. |
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Bending of light |
§9-10, |
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Operations on 4-vectors |
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Perihelion shift of Mercury |
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Orbits. Path of light rays |
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Robertson-Walker metric, Hubble’s Law, red shift |
§17-18, H |
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Feb |
Friedman’s equation |
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Comoving coordinate vs.
redshift |
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Weighing the universe with
supernovae |
§19 |
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14 |
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Midterm
exam Midterm2010 MidtermAns2010 |
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Cosmic
microwave background radiation |
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Wilkinson
Microwave Anisotropy Probe, angular scale of anisotropy |
http://map.gsfc.nasa.gov/ |
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Sound
waves |
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Mar |
Dicke’s conundrums, inflation |
§19.2, PR |
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Spring break |
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Einstein’s
Equations |
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Equivalence principle: “the
happiest thought in my life”— Einstein. Equation of motion with gravity. Noether’s theorem. |
§6.2 |
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Experimental
foundation of the theory of gravity; Eötvös’ & Dicke’s experiments |
§6.1 |
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Path to Einstein’s
equation; Transformation
of tensors; derivative of a tensor |
§20, Weinberg, G&C,
§2.1 & §4.1, 4.2, 4.3, 4.6 |
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Parallel
transport of a vector; Riemann-Christoffel
curvature tensor |
§21.3, Weinberg, G&C,
§6 |
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Bianchi
Identity. Stress-energy tensor. Conservation of energy
& momentum. |
§22 |
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Einstein’s
discovery of the field equation. Schwarzschild metric, derivation of |
§21.4, §9-16 in Pais |
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Robertson-Walker
metric, derivation of |
OHanian & Ruffini: §9.7-9.8 |
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Apr |
Friedman’s
equation, derivation of |
Weinberg, G&C, §15.1 |
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Gravitational
waves |
§16 |
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Wave
equation. |
§21.5 |
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Emission
of gravitational waves. The Hulse-Taylor pulsar |
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17 |
19 |
Black
holes. Eddington-Finkelstein coordinates.
Thermodynamic temperature. Hawking emission. |
§12, 13.3, Page |
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24 |
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Discovery
of black holes. Relativistic stellar models. |
§14, §24 |
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26 |
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Missouri
Club |
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Final
exam, Mon., April 30, 3:00-5:00, BPS1308 |
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The first part of AST860 introduces cosmology and
the solar-system effects of gravity by using the metric (and a few results from
the field equations), without the full machinery of the field equations. The solar
system effects are bending of light, time dilation, the perihelion shift of
Mercury, and the Shapiro effect. The cosmological effects are Hubble’s Law, red
shift, distance and time, flux, and angular measurements. The second part of
the course develops the field equations as Einstein did, through the
Equivalence Principle (the “happiest thought in my life” according to
Einstein). In the third part of the course are modern topics in gravitational
astrophysics: inflation, the fluctuations in the cosmic background radiation,
and gravitational radiation. Other topics are the experimental foundation of
the theory of gravity and black holes.
The
course grade will be based on homework (20%), midterm (30%), and the final exam
(50%). Your lowest homework score will be dropped. You may work together on
your homework assignments, but you must hand in your own solutions. Late
homework may be handed in up until the time the graded papers are returned. On
each homework assignment, one question will be graded. Check your answers on
the other questions yourself.