Advances in Lorentzian geometry

Lorentzian geometry is an active field of mathematical research with particular relations to relativity theory. The main purpose of this exposition is to present novel results in a concise overview and to provide a kind of mind map of the research done by the community today. We hope in particular that this little book serves young researchers who are interested in this topic as a valuable source for information on the frontiers of this field. It includes articles and surveys covering a large variety of topics in Lorentzian geometry, amongst which are: Submanifolds of particular causal character, Killing and conformal vector fields, warped products and foliations, Einstein equations, energy conditions and black holes, techniques from Riemannian geometry, algebraic classification of spacetimes.