PHYS 516 :: Physics Illinois :: University of Illinois at Urbana-Champaign

Course Description

What is this class about?

General Relativity 2 is an advanced graduate course in advanced topics in Einstein's theory of General Relativity, focusing on non-spinning and spinning black holes, the 3+1 decomposition of the Einstein equations and the ADM formulation, extreme mass-ratio inspirals and black hole perturbation theory. Other topics, such as physical cosmology, gravitational wave astrophysics and comparable-mass compact binaries, will be covered in other graduate GR courses. This class is a very mathematically intensive, because it has to be to achieve its goals, and it will use technical language, as defined in General Relativity I (see e.g., Carroll's textbook), which is heavily employed in the gravity and astrophysics scientific literature.

What is this class not about?

In short, this is not an easy class, because it has to be of a certain difficulty to achieve its main goal: to teach you all of the advanced tools you will need to make breakthroughs in your research. Therefore, this class is not a core course, or a superficial survey of advanced topics. Although the class is not easy, it is also not beyond the ability of intermediate or advanced graduate students, provided you devote the time required to do the work needed to learn the tools you will need to succeed.

Who should take this class?

This course is intended for all intermediate or advanced graduate students with an interest in gravity, astrophysics, high energy physics or string theory. As such, it is assumed students 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, as well as knowledge of the basics of general relativity. The purpose of the class is to prepare students for research in (analytical or numerical) general relativity, relativistic astrophysics, gravitational waves, and cosmology, as well as black hole-related topics in high-energy physics and string theory. Other students with broader interests are welcomed to take this class, but they should be advised that there are 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, complete all homework assignments and complete a final exam (see the course schedule). In addition, students are expected to be mature enough to independently do some amount of self-learning outside of class, including reading the assigned book on their own (see below), reading papers mentioned in class, and doing homework discussed in the book but not explicitly solved in lecture (including optional assignments if depth is sought). Since this is a graduate course, readings will not be assigned weekly, but rather, students are expected to find the topics in the course's textbook that are being covered in class and read about them; in addition to the required class textbook, there are also other (recommended) textbooks that students can and should refer to if and when needed. Students will be required to do a very high amount of homework (much more than in their regular core classes), with assignments starting easy and light, but with the difficulty and the amount of homework increasing with the flow of class. Therefore, please expect the initial homework load to seem "easy,'' but rest assured that the more complicated homework that will really hone your research skills will come. Questions are always welcomed, either in class, or outside of class during office hours.

Texts

The main textbook of this course is:

Suggested complementary reading includes:

Technical papers and review articles for further reading will be suggested during the lectures.

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.