Classes	TuTh 10:20-11:40, 1308 BPS.
Instructor	Mr. Ed Loh, 3260 BPS, 884-5612, Loh@msu.edu
Office hours	TuTh 11:50-1:00, 3260 BPS, or as scheduled.
Textbook	Gravity, J. B. Hartle, Addison-Wesley, 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	angel.msu.edu

Dates				Topic	Reading
Elementary gravity
	12		Jan	Introduction, lessons of special theory that apply to gravity, Minkowski metric, Schwarzschild metric	§1-5
		14		Gravitational redshift. Shapiro effect	PR, S
	19			Bending of light	§9-10,
		21 H1	H1A	Operations on 4-vectors
	26			Perihelion shift of Mercury
		27		Orbits
	2 nb		Feb	Path of light rays
	2 nb			Robertson-Walker metric, Hubble’s Law, red shift	§17-18, H
		4 H2	H2A	Friedman’s equation
	9			Comoving coordinate vs. redshift
		11 H3	H3A	Weighing the universe with supernovae	§19
	16		M MAns	Midterm exam
		18		Cosmic microwave background radiation
	23	25		Wilkinson Microwave Anisotropy Probe, angular scale of anisotropy	http://map.gsfc.nasa.gov/
	2 H4		Mar H4Ans	Dicke’s conundrums, inflation	§19.2, PR
Einstein’s Equations
		4		Equivalence principle: “the happiest thought in my life”— Einstein. Equation of motion with gravity. Noether’s theorem.	§6.2
				Spring break
	16			Experimental foundation of the theory of gravity; Eötvös’ & Dicke’s experiments	§6.1
		18		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
	23			Parallel transport of a vector; Riemann-Christoffel curvature tensor; Bianchi Identity	§21.3, Weinberg, G&C, §6
		25 H5	H5Ans	Stress-energy tensor. Conservation of energy & momentum. Einstein’s discovery of the field equation	§22, §9-16 in Pais
	30			Schwarzschild metric, derivation of	§21.4
		1	Apr	Robertson-Walker metric, derivation of	OHanian & Ruffini: §9.7-9.8
	6			Friedman’s equation, derivation of	Weinberg, G&C, §15.1
		8 H6	H6Ans	Gravitational waves	§16
	13			Wave equation.	§21.5
		15 H7		Emission of gravitational waves. The Hulse-Taylor pulsar	§23, §11.3, T, H, TW
	20A 20B	22 H8		Black holes. Eddington-Finkelstein coordinates. Thermodynamic temperature. Hawking emission.	§12, 13.3, Page
	27	29			§14, §24
				Final exam, Mon., May 3^rd, 10:00-12:00, BPS1308

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.