Introduction to General Relativity
This course provides an introduction to Einstein’s theory of gravity, known as General Relativity. The initial part focuses on the mathematical tools in field theory, differential geometry, and tensor calculus necessary to formulate the theory and arrive at the Einstein equations. The remainder of the course explores specific solutions to the Einstein equations and their properties, including black holes, gravitational waves, and cosmological spacetimes. A series of compulsory exercises accompanies the course. This course is a recommended precursor to the „Advanced General Relativity“ course typically offered in the following semester.
- Lecture notes
GRlecture01.pdf, GRlecture02.pdf, GRlecture03.pdf, GRlecture04.pdf, GRlecture05.pdf, GRlecture06.pdf, GRlecture07.pdf, GRlecture08.pdf, GRlecture09.pdf, GRlecture10.pdf, GRlecture11.pdf, GRlecture12.pdf, GRlecture13.pdf, GRlecture14.pdf, GRlecture15.pdf, GRlecture16.pdf, AdvancedGeometry.pdf, MaurerCartan.pdf - Exercise problems
GRexercise01.pdf, GRexercise02.pdf, GRexercise03.pdf, GRexercise04.pdf, GRexercise05.pdf, GRexercise06.pdf, GRexercise07.pdf, GRexercise08.pdf, GRexercise09.pdf, GRexercise10.pdf, GRexercise11.pdf, GRexercise12.pdf
Advanced General Relativity
The course focuses on dynamic solutions to Einstein’s field equations relevant to both cosmology and astrophysics. It covers solutions for expanding universes, rotating compact objects—such as black holes and neutron stars—and the collapse leading to black hole formation. A series of compulsory exercises accompanies the course. Building on topics from the recommended precursor, „Introduction to General Relativity“, this course provides the essential tools for research in General Relativity.
- Lecture notes
AGRlecture01.pdf, AGRlecture02.pdf, AGRlecture03.pdf, AGRlecture04.pdf, AGRlecture05.pdf, AGRlecture06.pdf - Exercise problems
AGRexercise01.pdf, AGRexercise02.pdf, AGRexercise03.pdf, AGRexercise04.pdf, AGRexercise05.pdf, AGRexercise06.pdf, AGRexercise07.pdf, AGRexercise08.pdf, AGRexercise09.pdf, AGRexercise10.pdf
Numerical Holography
Slides and Tutorials of the lecture series held at the DKPI summer school in Zwettl (Austria) 16-20 Sep. 2019
- Slides: NumHolZwettl2019.pdf
- Mathematica tutorial files: Tutorial.tar.gz
(The files „tutorial_x_exercise.nb“ contain exercises for the students, where the files „tutorial_x_sol.nb“ contain the solutions to these exercises.)
Student Projects
- since Feb. 2026 Sinan Altiparmak, PhD Student, Goethe University
PhD Thesis (preliminary): Gravitational Waves from Binary Neutron Star Mergers (pdf) - Jan. 2025 – Jan. 2026 Sinan Altiparmak, Master Student, Goethe University
Master Thesis: Generic finite temperature extension of the neutron star equation of state (pdf) - Jan. 2023 – Jan. 2024 Alina Stehr, Master Student, Goethe University
Master Thesis: Impact of Quark Matter Formation in the Prompt Collapse in Binary Neutron Star Mergers (pdf) - Sep. 2021 – Apr. 2022 Sinan Altiparmak, Bachelor Student, Goethe University
Bachelor Thesis: On the Speed of Sound in Neutron Stars (pdf) - Mar 2020 – Jun 2020 Jonah Post, Bachelor Student, Leiden University
Bachelor Thesis: Lax Entropy Conditions for the One-Dimensional Riemann Problem (pdf) - Apr 2016 – Jul 2020 Philipp Stanzer, Graduate Student, TU-Wien
PhD Thesis: Numerical Relativity, Holography and the Quantum Null Energy Condition (pdf) - Apr 2015 – Mar 2016 Philipp Stanzer, Master Student, TU-Wien
Master Thesis: Entanglement Entropy in Heavy Ion Collisions (pdf, awarded with student price of Austrian Physical Society) - Apr 2015 – Jun 2016 Ognen Kapetanoski, Master Student, TU-Wien
Master Thesis: Entanglement entropy of a compact region in a 2D-dilaton gravity theory (pdf)