General Information

A continuation of PHYS 6553 and ASTRO 6509 that covers a variety of advanced topics and applications of general relativity in astrophysics, cosmology, and high-energy physics.

Prerequisites

PHYS 6553 or permission of instructor.

Topics Covered

  • Black hole thermodynamics
  • Other advanced topics in black hole physics such as rotation, perturbations, merger and ringdown, superradiance, singularity theorems, and properties of the horizon.
  • de Sitter and anti-de Sitter spacetimes
  • The mathematics of hypersurfaces and geodesic congruences
  • Energy and the Hamiltonian in GR

Workload

  • 10 Problem sets ~5-15hours/week, and a final presentation. [SP23]
  • The workload for this class is honestly really chill. There were a total of 5 psets, each of which took maybe 10 hours, and one final project. There were no exams. Compared to the first semester GR course. This was nothing. [SP25]
  • 10-12 hrs/week, 5 problem sets, one final presentation and paper [SP25]

General Advice

  • Easier than the first general relativity course. [SP23]
  • I recommend giving this class a try if it at all aligns with your research experience! [SP25]
  • If you made it through GR 1, you can make it through GR 2. I personally wasn’t initially as much of a fan of GR 2 as the first class (since it turned out to be a a lot more abstract and mathy), but when we covered the really exciting and interesting topics, I found that same spark I had in the first class. The problem sets, as usual, were moderately difficult, with most of them taking around 10-12 hours, but compared to the first class it feels like a nice break from having problem sets due every week.

The final topic (which in our case was spinors) was something that was added at the last minute; we were initially going to cover Hawking Radiation, but in the end it is up to whatever the professor chooses. Overall, I really enjoyed this class and would highly recommend! [SP25]

Testimonials

  • Very fun; we covered Hawking radiation at the end, but the topics vary year to year. [SP23]
  • I strongly recommend this course to anyone interested in GR related research, either astrophysical, theoretical, or other. Once you have taken one semester of GR, this course is really accessible. Professor Hartman is awesome. I would say it helps to make friends in the class to discuss homework or other work together. We used “A Relativist’s Toolkit” by Poisson. [SP25]
  • I really enjoyed this class! It’s simultaneously harder than GR 1 due to the advanced topics that we cover, and easier, since there’s a lot less overall work that we do. In terms of content, we covered roughly the following (in order): Reissner Nordstrom (charged) Black Holes, Submanifolds and Hypersurfaces, Kerr (spinning) Black Holes, The Hamiltonian in GR, Geodesic Congruences, de Sitter Spacetime, Spinors in Curved Spacetime [SP25]

Past Offerings

Semester Professor Median Grade Syllabus
Spring 2023 Tom Hartman N/A PHYS6554_SP23.pdf
Spring 2025 Tom Hartman N/A PHYS6554_SP25.pdf