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

Null Hypersurfaces in Kerr-Newman-AdS Black Hole and Super-Entropic Black Hole Spacetimes