This is an intensive course aimed primarily at Master's and PhD students in gravitational/high-energy/astro-particle/mathematical physics. Advanced Bachelor's students are also encouraged to attend. The course assumes comfort with derivations and calculations in general relativity/pseudo-Riemannian geometry. Due to the variety of background of expected audience and time limit, proofs will not be presented during the lecture. **Students are strongly encouraged to approach me during office hours so as to not fall behind on understanding.**

Course spacetime coordinates: Tuesday 7th June 2022 - Friday 10th June 2022, Lecture Hall 267, Appelstrasse 2

2 x 2hr lectures a day: 10:00 - 12:00 CET and 14:00 - 16:00 CET

Email:

Office: 208B

Office hours: 16:00-18:00

- General relativity or knowledge of differentible pseudo-Riemannian manifolds
- Knowledge of mathematica/maple will be advantageous
- Mode expansions in QFT following the first few chapters of Srednicki's book will be useful

- Stellar Collapse
- Black Hole Geometries and Geodesics in 4d
- Black Hole Mechanics
- Black Hole Thermodynamics and Evaporation

- Wald - General Relativity
- Hawking & Ellis - Large Scale Structure of Spacetime
- Sachs & Wu - General Relativity for Mathematicians
- Carroll - Spacetime and Geometry
- Lecture Notes by Matthias Blau (link to website, not .pdf file)
- O'Neill - Semi-Riemannian Geometry

Paul Townsend's lecture notes and Piotr Chruschiel's notes on the geometry of black holes are all time classics and my personal favourites.

Handwritten notes can be found here. Warning: File is roughly 15MB in size. Typos observed during lectures not corrected yet.

Gravitational collapse of cold stars beyond quantum degeneracy. Derivation of the Schwarzschild solution.
Mathematica notebook for making your lives easier in tensor manipulation can be found here.

On continued gravitational collapse - R. Oppenheimer, H. Snyder (Original paper on model of stellar collapse leading to black hole formation in four dimensions)

The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics - Elliott Lieb & Horng-Tzer Yau (A rigorous derivation of the Chandrasekhar mass)

The Schwarzschild spacetime, extensions of the Schwarzschild spacetime

Treatment of stationary spacetimes:

- Stationary black holes by R. Beig and P. Chruschiel

Initial value problem

Singularity theorem

Penrose-Carter diagrams and conformal compactification

Reissner- Nordstrom black holes and Kerr Black Holes (We did not consider orbits around Kerr black holes)

More on the Kerr spacetime:

- The Kerr Spacetime: A Brief Introduction by Matt Visser
- Rotating black holes: Locallu non-rotating frames, energy extraction and scalar synchrotron radiation by James Bardeen and Saul Teukolsky (A time less classic). PDF available here.

Black Hole Mechanics

QFT in curved spacetime, Pair creation in a time dependent gravitational field, Hawking radiation and implications