  Recently it was discovered that null hypersurfaces can develop caustics
outside the event horizon of super-entropic Kerr-AdS black holes, in contrast
to the usual Kerr-AdS case. In this work we explore a few more examples of
black hole spacetimes in which such exterior caustics can develop. If a closed
null curve is present, e.g., in the case of Taub-NUT and the "transunital"
Kerr-AdS spacetimes, then it coincides with a null hypersurface caustic (NHC)
of a minimal separation parameter. Thus a spacetime on the verge of forming
closed timelike curves could develop a caustic. Known examples of
super-entropic black holes also have exterior NHC, although such spacetimes are
free of closed null/timelike curves. Nevertheless the relationship between
closed causal curves, NHC, and super-entropy is not straightforward. This is
best illustrated with the BTZ black string, which for some choices of the warp
factor in the extra dimension and the value of the charge, can be
super-entropic. However, even those that are not super-entropic can admit NHC
outside the horizon.
