Global view of kinks in 1+1 gravity

Following Finkelstein and Misner, kinks are nontrivial field configurations of a field theory, and different kink numbers correspond to different disconnected components of the space of allowed field configurations for a given topology of the base manifold. In a theory of gravity, nonvanishing kink numbers are associated with a twisted causal structure. In two dimensions this means, more specifically, that the light cone tilts around (nontrivially) when going along a noncontractible non-self-intersecting loop on spacetime. One purpose of this paper is to construct the maximal extensions of kink spacetimes using Penrose diagrams. This will yield surprising insights into their geometry but also allow us to give generalizations of some well-known examples such as the bare kink and the Misner torus. However, even for an arbitrary 2D metric with a Killing field we can construct continuous one-parameter families of inequivalent kinks. This result has already interesting implications in the flat or de Sitter case, but it applies, e.g., also to generalized dilaton gravity solutions. Finally, several coordinate systems for these newly obtained kinks are discussed.