PHYS 515 :: Physics Illinois :: University of Illinois at Urbana-Champaign
Course Description
What is this class about?
General Relativity is an advanced graduate course that teaches the foundations of Einstein's theory of General Relativity, with emphasis on modern coordinate-free methods of computation. This class is a very mathematically intensive, laying the foundations for black hole theory, post-Newtonian theory and numerical relativity. 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 mathematically intensive. 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 (very 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, physical cosmology and astrophysics.
Who should take this class?
This course is intended for advanced (2nd year and higher) graduate students, although (highly-motivated) first-year graduate students, or advanced undergraduate students are also welcomed (provided they have fulfilled the pre-requisites for the course). All students are assumed to 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. 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, 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 welcomed 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, complete all homework assignments and complete a midterm exam and 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 (see below), reading papers mentioned in class, and watching video lectures recorded by Prof.~Yunes. 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 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.
Texts
At the level of "Spacetime and Geometry" by Sean Carrol (Pearson Press). Other recommended texts listed 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.