Syllabus: General Relativity (PHY 6938) - Spring 2026

Instructor: Wolfgang Tichy
Office: Science and Engineering (SE) 444
E-mail: wolf "at" fau.edu (be sure to put PHY 6938 in the subject line)
Phone: 7-3387
Class Website: https://wolf.mathprotutoring.com/Teaching/2026_GR/index.html

Office Hours: Tuesday 3:30pm-5:00 pm, Thursday 3:30-5:00 pm

Textbooks:
S. M. Carroll, An Introduction to General Relativity Spacetime and Geometry (Pearson/Addison Wesley, 2004)
A. P. Lightman, W. H. Press, R. H. Price and S. A. Teukolsky, problem book in relativity and gravitation (Princeton University Press, 1975)

Other books worth looking at:
C. Misner, K. Thorne and J. Wheeler, Gravitation (Freeman, 1973)
R. Wald, General Relativity (Chicago, 1984)
S. Weinberg, Gravitation and Cosmology (Wiley, 1972)
P. A. M. Dirac, General Theory of Relativity (Wiley, 1975)

Course objectives:
The course will give an overview of General Relativity. It is intended to be a first graduate course in General Relativity. The course is self contained and no particular prerequisite is required. However, some prior knowledge of Special Relativity will be helpful. In the course of a review of Special Relativity, the student will be introduced to a number of mathematical tools used in General Relativity. These tools will then be used to discuss gravitation as spacetime curvature. The goal is to study black holes, gravitational radiation, as well as some cosmology. The lectures will set the pace for the course, but problem solving is an essential part of this course. The students are expected to study on their own by reading assigned texts and by solving assigned problems.

Topics covered:

1. Special Relativity and Flat Spacetime:
   spacetime, metric, proper time, Lorentz transformations, worldlines, vectors, tensors
2. Manifolds:
   maps, continuity, open sets, charts and atlases,manifolds, differentiation, vectors as derivatives, tensors again, volume forms and integration
3. Curvature:
   covariant derivatives and connections, connection coefficients, Christoffel connection, parallel transport, geodesics, affine parameters, Riemann curvature tensor, geodesic deviation
4. Gravitation:
   gravitation as spacetime curvature, Einstein's equations, the Hilbert action, Principle of Equivalence, Cosmological constant

1. The Schwarzschild Solution and Black Holes:
   spherical symmetry, Schwarzschild metric, Birkhoff's theorem, geodesics of Schwarzschild, event horizon, black holes, charged black holes, cosmic censorship, rotating black holes, Penrose and black hole thermodynamics
2. Weak Fields and Gravitational Radiation:
   the weak-field limit defined, gauge transformations, linearized Einstein equations, gravitational plane waves, gravitational radiation by sources, energy loss
3. Cosmology:
   homogeneity and isotropy, Robertson-Walker metric, Friedmann equations, evolution of the scale factor, redshift, Hubble's law
4. The 3+1 formalism and numerical relativity:
   3+1 split of spacetime, extrinsic curvature, ADM evolution and constraint equations, initial data

Homework: All homework problems will be posted on the class website. Only about one third of all problem sets will be graded. The due dates for the graded problem sets will be posted on the class website. You will loose about 10% of the maximum score for each day your homework is late. Please note that it is essential that you do all problem sets (graded or not). This is the only way for you to learn.
Homework policy: You must solve the problems yourself. This is the optimal way to learn the material. If you are stuck on a problem you may discuss it with other students or the instructor. However, this discussion should be limited to understanding the essential point(s) so that you can go ahead and solve most of the problem yourself. In particular, do not use solution sets from problem/solution books, or any other sources where you can simply look up your homework problems!

Grades will be based on the following:

Activity	Percentage
Homework	25%
Class Participation	5%
Midterm Exam	30%
Final Exam	40%

Tentative exam dates:
Midterm Exam: 3/24/2026 in class
Final Exam: 5/5/2026 from 1:15pm - 3:45pm in SE 319
Exam Make up policy:
In general any missed exam will count as if the student had obtained zero points. If the student can convince the instructor that the exam was missed for a good reason, the student's grade will be computed from the remaining exams and homework.

Strange Florida law issues:

Students enrolled in this course may be allowed to record video or audio of class lectures in certain cases. To find out more, read the official university policies.
But even in allowed cases, it is much more polite (and also prudent) to ask for instructor agreement before starting to record.

FAU policy statements:
Please see the so called "Simple Syllabus" in Canvas for all official FAU policies.