The limit of Kerr-de Sitter spacetime with infinite angular-momentum parameter $a$

TL;DR

This paper investigates the limit of Kerr-de Sitter spacetime as the angular momentum parameter approaches infinity, revealing a unique solution with distinctive horizon and global structure properties.

Contribution

It introduces a new exact solution for the Einstein equations with positive cosmological constant in the infinite angular momentum limit, detailing its global and horizon structure.

Findings

The spacetime is Petrov type-D with conformally flat scri.

Horizons are foliated by non-compact marginally trapped surfaces.

The solution has a unique free parameter related to angular momentum.

Abstract

We consider the limit $a\rightarrow \infty$ of the Kerr-de Sitter spacetime. The spacetime is a Petrov type-D solution of the vacuum Einstein field equations with a positive cosmological constant $\Lambda$, vanishing Mars-Simon tensor and conformally flat scri. It possesses an Abelian 2-dimensional group of symmetries whose orbits are spacelike or timelike in different regions, and it includes, as a particular case, de Sitter spacetime. The global structure of the solution is analyzed in detail, with particular attention to its Killing horizons: they are foliated by non-compact marginally trapped surfaces of finite area, and one of them `touches' the curvature singularity, which resembles a null 2-dimensional surface. Outside the region between these horizons there exist trapped surfaces that again are non-compact. The solution contains, apart from $\Lambda$, a unique free parameter which can be related to the angular momentum of the non-singular horizon in a precise way. A maximal extension of the (axis of the) spacetime is explicitly built. We also analyze the structure of scri, whose topology is $\mathbb{R}^3$.