Matthias Plaue Book order

The Gödel spacetime is an important cosmological solution of Einstein's field equations of gravitation. Although it does not offer a viable description of the physical universe, it illustrates the theoretical possibility of time travel. This work investigates world models similar to the Gödel spacetime with particular emphasis on relations between kinematical properties (shear, vorticity, acceleration, expansion) and causality violation, i. e., the formation of closed timelike curves.

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.