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

angel.msu.edu

 

Dates

Topic

Reading

Elementary gravity

 

 

10

 

Jan

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

§1-5

 

 

12

 

Gravitational redshift (Pound-Rebka). Shapiro effect.

PR, S

 

17

 

Bending of light

§9-10,

 

 

19

Operations on 4-vectors

 

 

24

H1

H1A

Perihelion shift of Mercury

 

 

 

26

 

Orbits. Path of light rays

 

 

31

H2

H2A

Robertson-Walker metric, Hubble’s Law, red shift

§17-18, H

 

 

2

Feb

Friedman’s equation

 

 

7

H3

H3A

Comoving coordinate vs. redshift

 

 

 

9

Weighing the universe with supernovae

§19

 

14

 

M

MAns

Midterm exam Midterm2010 MidtermAns2010

 

 

 

16

 

Cosmic microwave background radiation

 

 

21

23

 

Wilkinson Microwave Anisotropy Probe, angular scale of anisotropy

http://map.gsfc.nasa.gov/

 

28

H4

H4A

Sound waves

 

 

1

Mar

Dicke’s conundrums, inflation

§19.2, PR

 

 

 

 

Spring break

 

Einstein’s Equations

 

 

13

 

 

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

§6.2

 

15

 

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

§6.1

 

20

H5 H5A

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

 

22

 

Parallel transport of a vector; Riemann-Christoffel curvature tensor

§21.3, Weinberg, G&C, §6

 

27

H6

H6A

Bianchi Identity. Stress-energy tensor. Conservation of energy & momentum.

§22

 

29

 

Einstein’s discovery of the field equation. Schwarzschild metric, derivation of

§21.4, §9-16 in Pais

 

 

Robertson-Walker metric, derivation of

OHanian & Ruffini: §9.7-9.8

 

3

 

Apr

H7

Friedman’s equation, derivation of

Weinberg, G&C, §15.1

 

 

5

H7A

Gravitational waves

§16

 

10

 

 

Wave equation.

§21.5

 

 

12

H8

H8A

Emission of gravitational waves. The Hulse-Taylor pulsar

§23, §11.3, T, H, TW

 

17

19

H9

H9A

Black holes. Eddington-Finkelstein coordinates. Thermodynamic temperature. Hawking emission.

§12, 13.3, Page

 

24

 

 

Discovery of black holes. Relativistic stellar models.

§14, §24

 

 

26

 

Missouri Club

 

 

 

 

Final

Final exam, Mon., April 30, 3:00-5:00, 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. On each homework assignment, one question will be graded. Check your answers on the other questions yourself.