Content: This year marks the 100th anniversity of Albert Einstein's genesis of general relativity, which has revolutionalised the way we think about space and time and is still our experimentally best verified theory of gravitation. This course will focus on the mathematical foundations of the theory and exhibit their relations to physical concepts. After motivating the physical relevance of curved spaces, we will review the necessary tools from differential geometry (manifolds, tensor fields, pseudo-Riemannian metrics, connection, geodesics, curvature). The Einstein equations will be derived both from physical considerations and from a variational principle. Some of the most important consequences of the theory will then be discussed: gravitational radiation, black holes (Schwarzschild spacetime), and cosmology (Friedmann-Lemaitre-Robertson-Walker spacetimes). Finally there should be time for a more advanced topic such as conformal infinity or the Cauchy problem for the Einstein equations. There is some flexibility in the course material and interested students are encouraged to complete in advance a survey on interests and previous knowledge on Blackboard:
https://lms.fu-berlin.de/
After registering, go to Courses -> FB Mathematik und Informatik -> Allgemeine Relativitätstheorie -> Enroll. The survey can be found under "Lehrveranstaltung".