Projectively non-singular horizons in Kerr-NUT-de Sitter spacetimes

TL;DR

This paper investigates special non-singular horizons in Kerr-NUT-de Sitter spacetimes, revealing their properties and how they enable a smooth, global extension of these spacetimes from past to future infinity.

Contribution

It identifies and analyzes projectively non-singular horizons in Kerr-NUT-de Sitter spacetimes, providing conditions for their existence and implications for spacetime extension.

Findings

Found that non-singular horizons are cosmological and non-extremal.

Showed that such horizons allow a global spacetime extension from ^- to ^+.

Extended the spacetime topology to  imes S_3 with smoothness except for a possible Kerr-like singularity.

Abstract

It was recently discovered that Killing horizons in the generic Kerr-NUT-(anti) de Sitter spacetimes are projectively singular, i.e. their spaces of the null generators have singular geometry. Only if the cosmological constant takes the special value determined by the Kerr and NUT parameters, and the radius of the horizon, then the corresponding horizon does not suffer that problem. In the current paper, the projectively non-singular horizons are investigated. They are found to be cosmological and non-extremal. Every projectively non-singular horizon can be used to define a global completion of the Kerr-NUT-de Sitter spacetime it is contained in. The resulting spacetime extends from $\mathcal{I}^-$ to $\mathcal{I}^+$, has the topology of $\mathbb{R}\times S_3$ and is smooth except for a possible Kerr-like singularity.