# PHYS 598 NST :: Physics Illinois :: University of Illinois at Urbana-Champaign

## Course Description

### What is this class about?

This course will cover the advanced topic of neutron stars, focusing on the their interior composition and astrophysical observables. Emphasis will be put on (i) calculations of the equation of state of nuclear matter at high densities and low temperatures, and (ii) the modeling of the gravitational field of neutron stars. The topics discussed will include a subset of the following: Tolman-Oppenheimer-Snyder equation, mass-radius curves, Hartle-Thorne approximation, moment of inertia, quadrupole moment and tidal deformability, universal relations and gravitational waves, basics of thermodynamics, white dwarfs/crust, empirical mass formula, N-body interactions, liquid-gas phase transition/van der Waals, chiral effective field theory, chiral mean field model, NJL, (non)linear sigma model, MIT bag model, conserved charges, symmetry energy expansion.

This class is advanced because it will assume the student is well-versed in classical and quantum mechanics (at the level of Goldstein's and Baym's textbooks), and familiar with the basics of statistical mechanics (at the level of Reif's textbook) and general relativity (at the level of Carrol's textbook). The latter two are not pre-requisites for this class, but concepts drawn from these subjects will be employed. Some familiarity with basic particle or nuclear physics (at the level of Griffiths' textbook) would also be useful.

### Who is this class *not*?

This will *not* be 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 nuclear physics, gravity, astrophysics, and high energy physics. 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, quantum mechanics and statistical mechanics, and advanced mathematics, including differential equations, advanced Calculus and advanced linear algebra, as well as knowledge of the basics of particle physics and \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 nuclear 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 (unless you are sick or have any symptoms of illness), complete all homework assignments and complete a final exam or final presentation (tbd). In addition, students are expected to be mature enough to independently do self-learning outside of class, including reading the suggested books and reviews on their own (see below), reading papers mentioned in class, and doing homework discussed in the books 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. As you will see below, there is no single required textbook, but rather a set of recommended books and reviews that students can and should refer to if and when needed. Students will be required to do a high amount of homework, with assignments starting easy and light, but with the difficulty and the amount of homework increasing with the flow of class. This should be manageable, but it won't be ``easy'' at all times. 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 later. Questions are always welcomed, either in class, or outside of class during office hours.

### Texts

All textbooks are recommended but not required. We will draw from most of them. You can find the list of recommended textbooks 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.