Content

This course is an introduction to one of the pillars of our modern understanding of nature: the theory of general relativity. General relativity is a theory of gravitation that is based on two principles: general covariance and the equivalence principle. The exploration of these concepts will take us to differential geometry, a topic that will occupy a significant portion of our time, and constitutes the foundation of the course. Once we have mastered differential geometry, the remaininig of our trip through general relativity will proceed downhill. We will discuss what singles out general relativity among many possible generally covariant theories that respect the equivalence principle, and how its predictions are in excellent agreement with observations from solar system to cosmological scales. Beyond these tests we shall also explore predictions that the theory makes, which have not been directly confirmed yet: the existence of black holes, and the phenomenon of gravitational radiation.

Instructor

Time and Location

Office Hours

Lecture Notes

Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6. Lecture 7, Lecture 8, Lecture 9 (Errata),
Lecture 10, Lecture 11, Lecture 12, Lecture 13, Lecture 14, Lecture 15, Lecture 16, Lecture 17,
Lecture 18, Lecture 19, Lecture 20, Lecture 21, Lecture 22, Lecture 23, Lecture 24, Lecture 25.
Lecture 26, Lecture 27, Lecture 28 (Last).

Homework

Weekly homework assignments are due every Thursday. In order to learn the subject, it is extremely important that you complete the homework.

1. Due 08/09/10: Exercise 1 (lecture 1).
2. Due 09/16/10: Exercises 2 (lecture 3) and 3, 4, 5 (lecture 4).
3. Due 09/23/10: Exercises 6, 7 (lecture 5) and 8, 9, 10, 11 (lecture 6).
4. Due 09/30/10: Exercises 12, 13, 14 (lecture 7) and 15, 16, 17, 18, 19, 20 (lecture 8).
5. Due 10/07/10: Exercises 21, 22 (lecture 9) and 22, 23, 24 (lecture 10).
6. Due 10/14/10: Exercises 25, 26, 27, 28 (lecture 11) and 29 (lecture 12).
7. Due 10/21/10: Exercises 30 (lecture 13), 31, 32, 33, 34, 35, 36 (lecture 14).
8. Due 10/28/10: None: Study for Midterm Exam
9. Due 11/04/10: Exercises 37, 38 (lecture 15), 37 and 38 (lecture 16) .
10. Due 11/11/10: Exercises 39 (lecture 17), 40, 41, 42 (lecture 18).
11. Due 11/18/10: Exercises 43a, 43b (lecture 19), 44, 45 (lecture 20).

Links (Diversions)

1. Lecture 2: A test of the equivalence principle. A demonstration of the equivalence principle.
2. Lecture 3: The cardinality of different sets. Note that the real numbers have the same cardinality as a plane, as illustrated by Peano's space-filling curves.
3. Lecture 9: Steuard Jensen's General Relativity with Torsion.
4. Lecture 13: A test of general relativity using radio links with the Cassini spacecraft.
5. Lecture 14: C. M. Will's The Confrontation between General Relativity and Experiment (Living Reviews in Relativity.)
6. Lecture 15: Gravity Probe B.
7. Lecture 20: Relativistic binary pulsar B1913+16: Thirty years of observations and analysis..
8. Lecture 28: Astrophysical evidence for the existence of black holes..

Requirements

Exams

Grading

Literature

• Sean M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Benjamin Cummings (2003).

• Sean M. Carroll, Lecture notes on general relativity.

• Robert M. Wald, General Relativity, University of Chicago Press.
• Misner, Thorne, Wheeler Gravitation, Freeman.
• Steven Weinberg, Gravitation and Cosmology, Cambridge University Press.

Academic Integrity

The Syracuse University Academic Integrity Policy holds students accountable for the integrity of the work they submit. Students should be familiar with the Policy and know that it is their responsibility to learn about instructor and general academic expectations with regard to proper citation of sources in written work. The policy also governs the integrity of work submitted in exams, in laboratories, and in assignments, as well as the veracity of signatures on attendance sheets and other verifications of participation in class activities. Serious sanctions can result from academic dishonesty of any sort. For more information and the complete policy, see http://academicintegrity.syr.edu.

Academic Accommodation

Students who are in need of disability-related academic accommodations must register with the Office of Disability Services (ODS), 804 University Avenue, Room 309, 315-443-4498. Students with authorized disability-related accommodations should provide a current Accommodation Authorization Letter from ODS to the instructor and review those accommodations with the instructor. Accommodations, such as exam administration, are not provided retroactively; therefore, planning for accommodations as early as possible is necessary. For further information, see the ODS website, Office of Disability Services

Syracuse University
Office of Disability Services
804 University Avenue Room 309
Syracuse, New York 13244-2330
Phone: Voice: (315) 443-4498
TOO: (315) 443-1371
E-Mail: odssched@syr.edu