General Relativity, Winter Semester 2025/26

Prof. Dr. Joachim Lohkamp; Tutorial: Matthias Kemper

Learnweb, course catalogue: Lecture, Tutorial

Monday and Thursday 12–14 in M4.
First lecture on Thursday, 16 October.

After a quick introduction to Special Relativity (mechanics and electrodynamics at a finite speed of light, mathematically modelled with a quadratic form of signature (1, 3)), we will get to know Einstein’s General Theory of Relativity, which unifies Special Relativity with gravity. Here, space-time is a Lorentz manifold (almost a Riemannian manifold, but with a (1, 3) quadratic form on every tangent space instead of a positive definite scalar product). The field equations formalise the interaction between space-time geometry and matter content.

We will discuss some special solutions of the field equations, describing, e.g., black holes or the whole universe, and then focus on global geometric aspects of General Relativity like the Hawking–Penrose Singularity Theorems (Nobel Prize 2020), the Positive Mass Theorem, and the time-symmetric case of the Penrose Inequality (the general case of which is still an open problem!).

Prerequisite for this lecture is a solid knowledge of differential geometry as usually taught in the lecture Differential Geometry I: You should understand concepts like manifolds, Riemannian metrics, geodesics, Jacobi fields and curvature. Knowledge of physics can be helpful, but is not required. Students of physics are welcome; this lecture is for the most parts complementary to the lecture of the same name offered by the physics department.

If you are interested in participating, please register in Learnweb.