Physics/Astronomy 226 (Winter 2010): General Relativity

Course information

Lecture Time: Tuesdays and Thursdays, 12:00-1:45 PM
Lecture Place: ISB, Room 356
Instructor: Prof. Stefano Profumo
Office hours: Thursdays 4:00-5:00 PM (or by appointment)

Course description

This course is a graduate level introduction to General Relativity that aims to develop the formalism and to provide a solid foundation in the physical meaning of the theory. Scope of the class is on the one hand to gain confortability with the mathematical language and tools used, and on the other hand to acquire the ability to understand both advanced texts and current published research.

Syllabus

Course outline

• Special Relativity and Flat Spacetime
• Elements of Differential Geometry
• Gravitation: Einstein's Equations
• Weak Fields and Gravitational Waves
• The Schwarzschild Solution and Black Holes
• Elements of Physical Cosmology

Textbooks and Online Material

Other suggested reading:

• Gravitationan and Cosmology by Weinberg (library reserve)
• A first course in General Relativity by Schutz (library reserve)
• General Relativity by Wald (library reserve)
• Introducing Einstein's Relativity by D'Inverno (library reserve)
• Gravitation by Misner, Thorne and Wheeler (library reserve)

• Carroll's Book Errata
• Notes on Differential Forms from Victor Guillemin's MIT course on "Theory of Differential Forms" (thanks to TJ Torres for bringing this to my attention!)
• Two in one: learn some Italian and some algebraic Topology here!!
• Two in one: learn some German and some GR by reading Einstein's original 1915 article on the "Field Equations of Gravitation"
• The original gravitational redshift discovery PRL paper by Pound and Rebka

Grading policy

Grading will be based on 5 homework exercises plus one take-home final exam. Each homework will consist of typically 2 exercises on the material discussed in class, or on complements to that material. The homeworks will be posted on the course web page during the quarter. One week after the homework is handed out, during the first half hour at the beginning of class two ''volunteers'' will either spontaneously step forward or (in the absence of volunteers) will be drafted by the Instructor to solve the assigned problems, or to sketch the solution, on the blackboard. Volunteers will rotate throughout the class participants. Grading will be given according to the quality of both these oral presentations and the interaction/suggestions given to the volunteer when one is not at the blackboard (i.e. participation will be an important component).

The idea behind this homework and grading policy is to familiarize you with presenting orally your work, and in particular your research: doing this effectively is a fundamental skill and component to any research activity, both at the informal level of group meetings and at the more formal level of conference talks or job interviews. Interaction with those presenting their research is also a fundamental aspect of successful research. Further, this will give everybody an opportunity to discuss and re-think the assigned homework material, and to try to conceptualize and digest it in order to present it to others.

The final take-home exam will count 33% of the final grade, and will cover all the material discussed in class.

Homework exercises

(available by request from the Instructor)

Set number	Due Date	Solutions
1 (pdf)	- January 14 -	Solutions #1
2 (pdf)	- January 28 -	Solutions #2
3 (pdf)	- February 11 -	Solutions #3
4 (pdf)	- February 25 -	Solutions #4
5 (pdf)	- March 11 -	Solutions #5
Final Take-Home Exam (pdf)	- March 18 -