Research in Groups: Lorentz Geometry

Summer term 2016

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The WueCampus homepage of this RiG is now available.


In this Research in Groups, we discuss Lorentzian geometry: every manifold can be equipped with a Riemannian metric. However, it needs some additional features that a manifold can also be equipped with a Lorentzian metric, where the signature is now (+, -, ..., -). Such inner products on every tangent space are now the crucial ingredient for a geometric formulation of general relativity: our spacetime carries a Lorentz metric which encodes not only the propagation of light but the whole causal structure of the spacetime. We will discuss the geometry arising from such a metric in detail. Particular emphasize will be put on the causal structure, Cauchy hypersurfaces and globally hyperbolic spacetimes, and, if time permits, propagation of linear waves.

The course consists of essentially two components: first, a lecture where the basic notions of Lorentz geometry are explained. The preliminary program for the lecture component includes the following topics:

The second component will be a seminar by the students on more particular topics. We expect the participants to write a small proceeding-like summary of their seminar talks.


This Research in Groups addresses master students in mathematics or in mathematical physics with a reasonable background in differential geometry. Here the lecture notes on differential geometry from the last semesters will be a good starting point. They will be on WueCampus as soon as the course is enabled.

However, if you are in doubt, please contact me directly and we will find a solution. I will explain the necessary things either in the lecture part or directly.


The following list of references will be discussed in the first meeting. More references will be given individually.


If there are collisions with other lectures or seminars, please contact me early: maybe one can still shift things around a bit.


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