On the causal structure of stationary spacetimes in standard form with compact fiber

In this paper, we study stationary spacetimes in a form similar to standard stationary spacetimes, but which allow for the existence of closed timelike curves. In the case of compact fibers, we show a sufficient condition for these stationary spacetimes to be stably causal. This condition is invariant with respect to a change of slicing. In order to prove this result, we use Sobolev inequalities for differential forms. The condition contains a generally unknown constant that depends on the fiber, and we compute bounds for this constant for some important examples.