Regularity of a double null coordinate system for Kerr-Newman-de Sitter spacetimes

TL;DR

This paper develops a smooth double null coordinate system for Kerr-Newman-de Sitter spacetimes, enabling the extension of wave equation results from simpler black hole models to this more complex setting.

Contribution

It introduces a new smooth double null coordinate system for Kerr-Newman-de Sitter spacetimes, facilitating advanced analysis of wave equations in these geometries.

Findings

Constructed a smooth double null coordinate system for Kerr-Newman-de Sitter.

Proved the smoothness of intersection spheres in Boyer-Lindquist coordinates.

Extended wave equation results from Kerr and Reissner-Nordström to Kerr-Newman-de Sitter.

Abstract

We construct a double null coordinate system $(u,v,\theta_\star,\phi_\star)$ for Kerr-Newman-de Sitter spacetimes and prove that the two-spheres given by the intersection of the hypersurfaces $u=\mbox{constant}$ and $v=\mbox{constant}$ are $C^\infty$ in Boyer-Lindquist coordinates (including at the "poles"). The null coordinates allow one to immediately extend some results previously proven for Kerr. As an example, we illustrate how Sbierski's result, for the wave equation on the black hole interior, for Reissner-Nordstr\"{o}m and Kerr spacetimes, applies to Kerr-Newman-de Sitter spacetimes.