University of Minnesota
School of Physics & Astronomy

Phys 8501.001

General Relativity and Cosmology I

Lecture Notes
modified 6-Dec-2017 at 1:06PM by Joseph Kapusta
Notes_pp1-26.pdf | Download posted 5-Sep-2017 at 6:40PM
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Notes_pp172-182.pdf | Download posted 6-Dec-2017 at 1:06PM

Homework Problems
modified 5-Dec-2017 at 1:45PM by Joseph Kapusta
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modified 1-Sep-2017 at 7:39PM by Joseph Kapusta

There will be no examinations. The course grade will be based on weekly homework assignments and class attendance. Students are allowed to discuss the homework problems with each other. The rules are:

1. Each student must write up his or her own solutions.

2. List other students you discussed the problems with.

3. If you used any resources other than the required text, such as books, articles, web sites, past homework solutions, and so on, you must list them on your homework.

Office hours
posted 18-Aug-2017 at 9:56AM by Joseph Kapusta

In order to be as flexible as possible with office hours students can either make an appointment or stop by my office and I will be happy to help unless I am otherwise occupied.

Textbooks: Required and Recommended
modified 18-Aug-2017 at 9:48AM by Joseph Kapusta


Spacetime and Geometry: An Introduction to General Relativity, Sean Carroll (2003)

This is commonly used in graduate physics courses at major universities.

Recommended Classics

Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Steven Weinberg (1972)

This book favors the tensorial over the geometrical approach to make connection to non-gravitational physical theories.

Gravitation, Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler (1973)

Considered the encyclopedia of general relativity but not a textbook for the beginner.

The Large Scale Structure of Space-Time, S. W. Hawking and G. F. R. Ellis (1973)

This book focusses on geometry and singularities.

Recommended Alternatives

Gravity: An Introduction to Einstein's General Relativity, James B. Hartle (2003)

Less in-depth and usually adopted for undergraduate courses.

General Relativity, Robert M. Wald (1984)

A more modern approach than the classics but not for the beginner.

Ricci Mathematica notebook
posted 18-Aug-2017 at 9:50AM by Joseph Kapusta

Ricci is a Mathematica package for doing symbolic tensor computations that arise in differential geometry. It can be accessed at this website:

Appearance of Rapidly Moving Objects
modified 5-Sep-2017 at 6:21PM by Joseph Kapusta

These are a few references to the visual/photographic appearance of rapidly moving objects. The interested reader can find more by looking up the papers cited or by doing a Google search.

V. F. Weisskopf, Physics Today 19, September 1960, pp. 24-27.

F. R. Hickey, Am. J. Phys. 47, August 1979, pp. 711-714.

U. Krauss, January 2000, Brightness and color of rapidly moving objects: The visual appearance of a large sphere revisited.

A. Nowojewski, December 2005, Gamov's bicycle.

Lecture by Michel Janssen
modified 6-Nov-2017 at 8:39AM by Joseph Kapusta
Phys_8501-Janssen_lecture.pdf | Download posted 6-Nov-2017 at 8:39AM

White holes and wormholes
modified 29-Nov-2017 at 10:17PM by Joseph Kapusta

A nice introductory paper on this topic is: M. S. Morris and K. S. Thorne, American Journal of Physics 56, 395 (1988).

AJP_wormhole_paper.pdf | Download posted 29-Nov-2017 at 10:17PM

Matt Visser on Kerr spacetime
modified 6-Dec-2017 at 1:07PM by Joseph Kapusta
Visser_on_Kerr.pdf | Download posted 6-Dec-2017 at 1:07PM

General Relativity and Cosmology: Unsolved Questions and Future Directions
modified 12-Dec-2017 at 10:49AM by Joseph Kapusta

Universe publishes special issues on general relativity and cosmology. Many of the articles are open access, otherwise you need to access them through the university library using your X500 login.

Attached is just one nice article which should be easy reading.

Smoot_universe-02-00023-v2.pdf | Download posted 12-Dec-2017 at 10:47AM