Classes 
TuTh 2:404:00, 1308 BPS. 
Instructor 
Mr.
Ed Loh, 3260 BPS, 8845612, Loh@msu.edu 
Office
hours 
TuTh, 12:001:00, 3260 BPS, or as scheduled. 
Textbook 
Gravity, J. B. Hartle, AddisonWesley, 2003. Errata:
http://web.physics.ucsb.edu/~gravitybook/Errall.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 


Elementary gravity 




Jan 
Introduction, lessons of
special theory that apply to gravity, Minkowski
metric, Schwarzschild metric 
§15 




Gravitational redshift
(PoundRebka). Shapiro effect. 



Bending of light 
§910, 



Operations on 4vectors 



Perihelion shift of Mercury 





Orbits. Path of light rays 



RobertsonWalker metric, Hubble’s Law, red shift 
§1718, H 



Feb 
Friedman’s equation 



Comoving coordinate vs.
redshift 




Weighing the universe with
supernovae 
§19 


14 

Midterm
exam Midterm2010 MidtermAns2010 





Cosmic
microwave background radiation 




Wilkinson
Microwave Anisotropy Probe, angular scale of anisotropy 
http://map.gsfc.nasa.gov/ 


Sound
waves 



Mar 
Dicke’s conundrums, inflation 
§19.2, PR 





Spring break 

Einstein’s
Equations 





Equivalence principle: “the
happiest thought in my life”— Einstein. Equation of motion with gravity. Noether’s theorem. 
§6.2 



Experimental
foundation of the theory of gravity; Eötvös’ & Dicke’s experiments 
§6.1 


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 



Parallel
transport of a vector; RiemannChristoffel
curvature tensor 
§21.3, Weinberg, G&C,
§6 


Bianchi
Identity. Stressenergy tensor. Conservation of energy
& momentum. 
§22 



Einstein’s
discovery of the field equation. Schwarzschild metric, derivation of 
§21.4, §916 in Pais 



RobertsonWalker
metric, derivation of 
OHanian & Ruffini: §9.79.8 



Apr 
Friedman’s
equation, derivation of 
Weinberg, G&C, §15.1 



Gravitational
waves 
§16 




Wave
equation. 
§21.5 



Emission
of gravitational waves. The HulseTaylor pulsar 


17 
19 
Black
holes. EddingtonFinkelstein coordinates.
Thermodynamic temperature. Hawking emission. 
§12, 13.3, Page 


24 


Discovery
of black holes. Relativistic stellar models. 
§14, §24 


26 

Missouri
Club 




Final
exam, Mon., April 30, 3:005:00, BPS1308 

The first part of AST860 introduces cosmology and
the solarsystem 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.