PHYS 598 GR3 :: Physics Illinois :: University of Illinois at Urbana-Champaign

Course Description

What is this class about?

This course will cover advanced topics in Einstein's theory of General Relativity, focusing on the dynamics of compact binaries. Emphasis will be put on widely separated binaries of comparable mass ratio, where the post-Newtonian approximation is valid. The topics discussed will include a subset of the following: orbital dynamics of binary systems, three-body interactions and the Kozai-Lidov mechanism, the radiation-reaction force, gravitational waves emitted during inspiral. 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 GR I (see e.g. Carrol's textbook), which is heavily employed in the gravity and astrophysics scientific literature. 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 \emph{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 \emph{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 breakdown of topics below). 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

This course will primarily use " Gravity: Newtonian, Post-Newtonian, Relativistic" by Eric Poisson and Clifford Will (Cambridge University Press). Required and additional, recommended literature is listed under textbooks and in the syllabus.