Syllabus: PHY 6938 & PHY 4936 (General Relativity)

Department of Physics

Charles E. Schmidt College of Science

Florida Atlantic University

Fall 2004; PHY 6938 & PHY 4936, General Relativity (3 credits)

Class Location and Class Times:

Days Times Location

TR 5:00-6:20PM GS 116

Instructor: Warner A. Miller

Office: Science and Engineering (SE 442)

E-mail: wam@physics.fau.edu (be sure to put “PHY 6938 or 4936” in the subject line)

Class Website: http://www.physics.fau.edu/~wam/Fall04.html

Phone: 561-297-1189, or Debra at 561-297-3380

Office Hours:

Tuesdays: 2:00-3:30 PM, Thursdays 2:00-3:30 PM, or by appointment

(Note, Dr. Miller will make every effort to meet all office hours and will be available at these times in all but a few cases. Students may wish to call Dr. Miller prior to coming to his office to insure that he is in.)

Teaching Assistants:

There will not be a TA assigned to this class.

Required Text:

1. C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (W. H. Freeman and Co.; San Fancisco; 1998) (Note, section numbers below referr to this course).

Supplementary Material:

1. Occasionally Dr. Miller will provide class handouts to each student.
2. R. L. Bishop and S. I. Goldberg, Tensor Analysis on Manifolds (Dover Publ. Inc; New York; 1980).
3. B. F. Shutz, A First Course in General Relativity (Cambridge University Press; Cambridge, UK; 2000).

Course Objectives:

1. To overview Minkowski spacetime physics.
2. To motivate the transition to general relativity via an analysis of the equivalence principle.
3. To introduce the basics concepts of manifold theory and differential geometry with a stress on the physical interpretation of differential geometric objects that are essential for describing gravitational phenomenon.
4. To introduce Einstein’s equations and to trace their impact on physics in a curved spacetime.
5. To illustrate the resulting breakthroughs in our vision of physics as a whole. To present the most striking applications of general relativity, such as black holes, relativistic cosmology and possibly wormholes.

The student will be introduced to the geometric foundations of gravitation, will be introduced to the principle of equivalence, Mach’s principle and will gain an understanding of the origins and ramifications of Einstein’s field equations. The student will understand and work with tensor calculus with emphasis on the physical principles when applied to Minkowski spacetime geometries and curved pseudo-Reimannian geometries. The student will be able to understand the Einstein’s equations and will be able to solve, and manipulate these equations for certain problems (black hole geometries, Friedmann cosmologies, linearized gravitational waves). The student will be introduced to the stress-energy tensor and will understand how conservation of energy-momentum arises in general relativity. The student will be exposed to current research areas in general relativity (black hole astrophysics, numerical relativity, gravitational wave physics, worm holes and quantum gravity… ) throughout the course.

Brief Outline of Topics Covered:

1) Geometrodynamics: An Overview of Concepts and Key Insights?

Chapter 1

a. Spacetime.

b. Local Physics and Local Lorentzian Geometry.

c. Events and Coordinates.

d. Unity of Space and Time

e. Curvature

2) Physics in Flat Spacetime

Chapters 2.1-2.9, 6.1-6.6, 5.1-5.2, 5.5-5.10, 7.1-7.5

a. Minkowski Spacetime, Vectors, Forms and Tensors

b. Minkowski Metric, Interval, Light Cone, Inertial Frames

c. Accelerated Observers. Fermi Walker Transport.

d. Energy Momentum Tensor, Conservation of Momenergy, Equations of Motion. Perfect Fluid.

e. Incompatibility of Gravity and Special relativity

3) Riemannian Geometry

Chapters 8, 9.1-9.7,10.1-10.5,11.1-11.6,13.1-13.5,15.1-15.4

a. Differential Topology

b. Covariant Derivative, Parallel transport and Geodesics.

c. Geodesic Deviation and Curvature

d. The Metric

e. Bianchi Identitie and Contracted Bianchi Identities

4) Einstein’s Equations

Chapters 16.1-16.5 and 17.1-17.4 and 15.5-15.6.

a. Plausibility Arguments

b. The Hilbert Variational Principle

c. E. Cartan Moment of Rotation

5) Applications of Geometrodynamics

Chapters 18.1-18.3, 23.1-23.3, 25.1-25.6, 27.1-27.10

a. Weak Field Approximation.

b. Gravitational Waves in the Linearized Theory of Gravity.

c. The Schwarzschild Geometry, the Pit in the Potential.

d. Friedmann-Robertson-Walker Models, Cosmological Redshift.

Course Procedure:

Each class will begin with a lecture followed by interactive discussions and problem solving. Students may be asked to solve problems on the black board or work in groups.

Attendance Policy and Makeup Exams:

Dr. Miller wishes to emphasize that class participation is an integral part of this course. Students who miss a class should check with fellow students or contact the instructor to learn what they have missed. A student wishing to makeup an exam must contact Dr. Miller at least 1 hour before the start of the exam. You need to document (1) which exam you plan to miss, (2) why you are missing it, and (3) when you wish to make up the exam. If I do not speak with you before you miss the exam you will not be able to make up the exam.

Any or all of the exams may be given as a take-home exam at the discretion of the instructor.

Grading Criteria:ð

Letter grades will be based on the following:

Activity	Percentage
Exam #1	25% 25%
Exam #2
Homework	20% (10% deduction per day for late homework)
Final Exam	30%

Grading Scale:

Grade	Percentage
A	90-100
B	80-90
C	70-80
D	60-70
F	<60

Exam Dates: (Dates for Exam #1 and #2 are tentative)

Exam #1: September 16, 2004

Exam #2: October 19, 2004

Final December 7, 2004

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ð Exams and homework and grading metrics for PHY 6938 and PHY 4936 will be slightly different in order to account for the differences in levels of the class.