  A three-dimensional light-like foliation of a spacetime geometry is one
particular way of studying its light cone structure and has important
applications in numerical relativity. In this paper, we execute such a
foliation for the Kerr-Newman-AdS black hole geometry and compare it with the
lightlike foliations of the Kerr-AdS and Kerr-Newman black holes. We derive the
equations that govern this slicing and study their properties. In particular,
we find that these null hypersurfaces develop caustics inside the inner horizon
of the Kerr-Newman-AdS black hole, in strong contrast to the Kerr-AdS case. We
then take the ultra-spinning limit of the Kerr-Newman-AdS spacetime, leading to
what is known as a Super-Entropic black hole, and show that the null
hypersurfaces develop caustics at a finite distance outside the event horizon
of this black hole. As an application, we construct Kruskal coordinates for
both the Kerr-Newman-AdS black hole and its ultra-spinning counterpart.
