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

TL;DR

This paper studies null hypersurfaces in Kerr-Newman-AdS and super-entropic black holes, revealing caustic formations inside horizons and outside the event horizon, and constructs Kruskal coordinates for these spacetimes.

Contribution

It derives and analyzes null hypersurfaces in Kerr-Newman-AdS and super-entropic black holes, highlighting caustic development and providing coordinate constructions.

Findings

Null hypersurfaces develop caustics inside the inner horizon of Kerr-Newman-AdS.

Caustics form outside the event horizon in super-entropic black holes.

Kruskal coordinates are constructed for these black hole spacetimes.

Abstract

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.