Classes 
TuTh

Instructor 
Mr.
Ed Loh, 3260 BPS, 8845612, Loh@msu.edu 
Office
hours 
TuTh

Textbook 
Gravity, J. B. Hartle,
AddisonWesley, 2003 
Other
books 
Gravitation & Cosmology, S. Weinberg, 1972 (on
reserve at Business Library) Gravitation, Misner, Thorne, &
Wheeler, 1973 (on reserve at Business Library) 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 



12 

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



Gravitational redshift. Shapiro effect 




Bending of light 
§910, 



21 H1 
Operations on 4vectors 



26 


Perihelion shift of Mercury 



27 

Orbits 



Feb 
Path of light rays 





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



Friedman’s equation 





Comoving coordinate vs. redshift 




Weighing the universe with
supernovae 
§19 


16 

Midterm
exam 





Cosmic
microwave background radiation 




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



Mar
H4Ans 
Dicke’s
conundrums, inflation 
§19.2, PR 

Einstein’s
Equations 





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





Spring break 




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; Bianchi Identity 
§21.3, Weinberg, G&C,
§6 



Stressenergy tensor. Conservation of energy
& momentum. Einstein’s discovery of the field equation 
§22, §916 in Pais 




Schwarzschild
metric, derivation of 
§21.4 



Apr 
RobertsonWalker
metric, derivation of 
OHanian
& Ruffini: §9.79.8 




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



Gravitational
waves 
§16 




Wave
equation. 
§21.5 




Emission
of gravitational waves. The HulseTaylor pulsar 



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




§14, §24 





Final
exam, Mon., May 3^{rd}, 10:0012:00, 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.