Spacetime Splitting, Admissible Coordinates and Causality
  To confront relativity theory with observation, it is necessary to split
spacetime into its temporal and spatial components. The (1+3) timelike
threading approach involves restrictions on the gravitational potentials
$(g_{\mu \nu})$, while the (3+1) spacelike slicing approach involves
restrictions on $(g^{\mu \nu})$. These latter coordinate conditions protect
chronology within any such coordinate patch. While the threading coordinate
conditions can be naturally integrated into the structure of Lorentzian
geometry and constitute the standard coordinate conditions in general
relativity, this circumstance does not extend to the slicing coordinate
conditions. We explore the influence of chronology violation on wave motion. In
particular, we consider the propagation of radiation parallel to the rotation
axis of stationary G\"odel-type universes characterized by parameters $\eta >
0$ and $\lambda > 0$ such that for $\eta < 1$ ($\eta >1$) chronology is
protected (violated). We show that in the WKB approximation such waves can
freely propagate only when chronology is protected.
