  In this work we will focus on the causal character of Carter Spacetime (see
B. Carter, Causal structure in space-time, Gen. Rel. Grav. 1 4 337-406, 1971).
The importance of this spacetime is the following: for the causally best well
behaved spacetimes (the globally hyperbolic ones), there are several
characterizations or alternative definitions. In some cases, it has been shown
that some of the causal properties required in these characterizations can be
weakened. But Carter spacetime provides a counterexample for an impossible
relaxation in one of them. We studied the possibility of Carter spacetime to be
a counterexample for impossible lessening in another characterization, based on
the previous results.
  In particular, we will prove that the time-separation or Lorentzian distance
between two chosen points in Carter spacetime is infinite. Although this
spacetime turned out not to be the counterexample we were looking for, the
found result is interesting per se and provides ideas for alternate approaches
to the possibility of weakening the mentioned characterization.
