  Following Finkelstein and Misner, kinks are non-trivial 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, non-vanishing
kink-numbers are associated to a twisted causal structure. In two dimensions
this means, more specifically, that the light-cone tilts around (non-trivially)
when going along a non-contractible non-selfintersecting 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 like 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 deSitter case, but it applies e.g. also to generalized dilaton gravity
solutions. Finally, several coordinate systems for these newly obtained kinks
are discussed.
