PHYS 515 :: Physics Illinois :: University of Illinois at Urbana-Champaign

Course Description

What is this class about?

"Phys/Astr 515: Introduction to General Relativity" is an advanced graduate course that teaches the foundations of Einstein's theory of General Relativity. This class is mathematically intensive and lays the foundations for black hole theory, post-Newtonian theory and numerical relativity, but also gravitational wave physics or cosmology. In fact, General Relativity was initially taught in the mathematics department of universities! It is impossible to teach this subject without doing a deep-dive into the mathematics that are important in General Relativity, so the first half of this class is quite mathematical. Topics covered in the first half of the course include modern differential geometry, tensor analysis, and the foundations of General Relativity. The second half of the course presents the physical consequences of Einstein's theory, with a brief tour of its greatest hits: non-spinning (Schwarzschild) black holes and neutron stars, Solar System tests of gravitation, gravitational waves and linearized theory, and an introduction to cosmology. Students interested in these physical applications are encouraged to take subsequent courses on General Relativity, cosmology and astrophysics.

Who should take this class?

This course is intended for graduate students, although (highly-motivated) advanced undergraduate students are also welcome provided they have fulfilled the pre-requisites for the course. All students are assumed to have prior knowledge of Einstein's theory of special relativity, Newtonian gravitation and classical mechanics, Maxwell's theory of electrodynamics and advanced mathematics, including differential equations, advanced Calculus and advanced linear algebra. Other advanced mathematical machinery of General Relativity (e.g. differential geometry) will be covered in the course, and no computational knowledge is required. The primary target of the class is students who wish to specialize in General Relativity and gravitation (analytical or numerical), relativistic astrophysics and cosmology; this class will lay the foundations required to take more advanced classes and do research on the subject matter. The secondary target is students with broad interests in high-energy physics and phenomenology, nuclear theory, particle physics, condensed matter theory, field theory, string theory, and mathematical and computational physics; this class will provide a firm foundation in relativity and the ability to calculate in relativistic field theories. Other students with only a mild or minor interest in relativity are also welcome to take this class, but they should be advised that there may be other (perhaps less intensive) courses they can take to fulfill their elective requirements.

What is expected of students who take this class?

Students are expected to attend class and participate in discussions during class, complete all homework assignments and complete a midterm exam and a final exam. In addition, students are expected to be mature enough to independently do some amount of self-learning outside of class, including reading the assigned textbook(s) and papers mentioned in class. Since this is a graduate course, readings will not be assigned weekly, but students are expected to find the topics that are being covered in class in the course's textbook and read about them in the textbook; in addition to the required class textbook, there are also other additional (recommended) textbooks that students can and should refer to if and when needed. Questions are always welcomed, either in class, or outside of class during office hours.


This course will primarily use "Spacetime and Geometry" by Sean Carroll (Cambridge University Press). Required and additional, recommended literature is listed under textbooks and in the syllabus.

Academic integrity

All activities in this course are subject to the Academic Integrity rules as described in Article 1, Part 4, Academic Integrity, of the Student Code.