Seminar on Relativity and Black Holes, Summer Semester 2026
Prof. Dr. Joachim Lohkamp, Dr. Matthias Kemper
Preliminary meeting on Friday, 10 April 2026 at 12:30 in Lichthof, 3rd floor, Einsteinstr. 62.
Seminar presumably every other Thursday, 12:00–14:00.
The aim of this seminar is an introduction to the mathematical foundations of black holes.
We begin with special relativity. Under the assumption of a finite speed of light that is independent of the reference frame, it describes the motion of bodies in spacetime. Mathematically, this is ℝ4 equipped with a non-degenerate symmetric bilinear form, the so-called Minkowski space. Since measurements of time and length now depend on the observer, a number of surprising consequences arise.
Einstein's general theory of relativity unifies special relativity with gravitation. Here, a flat ℝ4 is no longer sufficient; instead, one needs curved spaces that can only be approximated locally by Minkowski space. We will take a closer look at the mathematical formulation of such objects. The relationship between gravitationally acting mass and the curvature of space is described by Einstein's field equations.
One of the first solutions to these field equations was published by Karl Schwarzschild in 1916. The Schwarzschild metric describes spacetime in the exterior region of planets or stars. If one continues this mathematical model into the interior, one soon encounters a threshold that an infalling particle can cross, but beyond which no light, nor anything else, can escape back outward: a black hole. The astonishing properties of this and related solutions will occupy us in the third part of the seminar. In particular, we want to examine what black holes look like as seen from up close.
This seminar is intended for bachelor's and master's students in mathematics, including those in the Master of Education program. Students of physics are also welcome. Prior knowledge of differential geometry or physics is helpful, but not required. Talks may be in German or English.
Preliminary meeting on Friday, 10 April 2026 at 12:30 in Lichthof, 3rd floor, Einsteinstr. 62. If you’re interested, feel free to enroll in the Learnweb course in advance. If you can’t join the preliminary meeting, please contact Matthias Kemper.