## PHYSH311B

GENERAL RELATIVITY

Steve Boughn

INTRODUCTION TO GENERAL RELATIVITY

The following information is not necessarily definitive but suggests the broad contours of the course

Textbooks:
A First Course in General Relativity by Bernard F. Schutz and Lecture Notes on General Relativity by S. Boughn.

Course Description:
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.