Null hypersurfaces in Kerr-(A)dS spacetimes

TL;DR

This paper derives equations for null hypersurfaces in Kerr-(A)dS spacetimes, showing they are caustic-free and useful for numerical black hole studies and coordinate definitions.

Contribution

It introduces a new method to construct null hypersurfaces in Kerr-(A)dS spacetime, extending previous work to include cosmological constant effects.

Findings

Null hypersurfaces are caustic-free for r>0.

Equations reduce to known cases when mass is zero.

Applications in numerical black hole simulations and coordinate systems.

Abstract

For many purposes, a three-dimensional foliation of spacetime is more advantageous to understanding its light cone structure. We derive the equations describing such foliations for the Kerr geometry with non-zero cosmological constant, and show that they reduce to null hypersurfaces in vacuum (anti-)de Sitter spacetime in the limit of zero mass. Furthermore, we find that these null hypersurfaces are free of caustics everywhere for $r>0$. Our construction has applications in numerical studies of rotating black holes, and in defining Kruskal coordinates for rotating black holes with non-zero cosmological constant.