INTRODUCTION TO GENERAL RELATIVITY
The following information is not necessarily definitive but suggests the broad contours of the course
A First Course in General Relativity by Bernard F. Schutz and Lecture Notes on General Relativity by S. Boughn.
The purpose of Phys 311a is a formal introduction to Einstein's Theory of General Relativity (GR). Upon completing this course, a student will be ready to tackle more advanced treatments of the subject, either in a course or through self study.
One can certainly get a "feeling" for GR without delving deeply into mathematics but rather by relying on analogies with curved surfaces in 3 dimensions. However, it can be convincingly argued that in order to truly "understand" a physical theory one must be able to perform calculations using the theory. To do this, one must be conversant in the mathematics of the theory. For this reason, about 40% of the course will be devoted to a treatment of differential geometry, the language of GR. This subject, although new to most of you, is not particularly difficult and is quite interesting and useful in its own right. All you need is a knowledge of calculus through partial differentiation and some knowledge of differential equations and linear algebra. The concepts of vectors, tensors, differential forms, Riemannian curvature, etc. will be developed in the course.
The course will begin with a review of special relativity (SR),
which will be expressed in the language of tensor analysis. I realize that
many of you have not studied special relativity in detail. Don't worry, our
discussion of SR will be self contained. After the development of differential
and Riemannian geometry, we will be able to study physics in a curved space-time
and finally arrive at Einstein's field equations, the heart of GR. These equations
are analogous to Newton's F = ma and F = Gm1m2/r2, and yet it will take 2/3
of the course to get to them. The remaining 1/3 of the course will be devoted
to the physical consequences of GR. Topics will include tests of GR, gravitational
waves, spherical stars, and black holes. Relativistic cosmology which is,
perhaps, the most important consequence of GR is the topic of another course
and will not be treated.
Several relativity texts will be placed on reserve in the Observatory library. Peter Bergmann's The Riddle of Gravitation is intended for the lay reader, but it is a delightful little book and can provide a welcome relief from the course's mathematical approach. Spacetime Physics by Taylor and Wheeler is an elementary treatment of special relativity for those who wish a more detailed "review" than will be offered in the course. Ohanian; Rindler; Lawden; and Burke are elementary texts in general relativity while Weinberg; Robertson and Noonan; Adler, Bazin, and Schiffer; and Misner, Thorne, and Wheeler (the "phone book") are more advanced texts. If you find something confusing in the lecture notes or in Schutz's text, don't hesitate to consult the reference books. The Principle of Relativity contains translations of some of the original papers by Einstein, Lorentz, Weyl, and Minkowski and reading them can be quite exciting. Finally, I have placed on reserve Georg Friedrich Bernhard Riemann's 1854 inaugural lecture entitled, "Uber die Hypothesen welche der Geometrie zu Grunde liegen" (in translation). It is a lecture that marked the beginning of Riemannian geometry on which general relativity is based. After you've studied differential geometry (first half of course), this will be an exciting paper to read.
Math 215, Linear Algebra (relevant topics in linear algebra will be developed in class). Physics 214b or some physics or chemistry course of comparable mathematical rigor. Math 204, Differential Equations, is desirable. Courses in either advanced classical mechanics and/or electromagnetism even if taken concurrently are also desirable.
Assignments, Projects, and Exams:
Weekly problem sets; two take-home exams; written report on a special topic in general relativity.