Characterization of (asymptotically) Kerr-de Sitter-like spacetimes at null infinity

TL;DR

This paper characterizes asymptotically Kerr-de Sitter-like spacetimes with positive cosmological constant at null infinity, using their initial data and properties of the Mars-Simon tensor, including cases with non-vanishing MST.

Contribution

It provides a new characterization of these spacetimes based on their initial data and the behavior of the Mars-Simon tensor, including cases with non-zero MST ambiguity.

Findings

Characterization of Kerr-de Sitter-like spacetimes via initial data on null infinity.

Analysis of the Mars-Simon tensor for different scalar functions Q.

Introduction of asymptotically Kerr-de Sitter-like spacetimes and their properties.

Abstract

We investigate solutions $(\mathcal{M}, g)$ to Einstein's vacuum field equations with positive cosmological constant $\Lambda$ which admit a smooth past null infinity $\mathcal{J}^-$ \`a la Penrose and a Killing vector field whose associated Mars-Simon tensor (MST) vanishes. The main purpose of this work is to provide a characterization of these spacetimes in terms of their Cauchy data on $\mathcal{J}^-$. Along the way, we also study spacetimes for which the MST does not vanish. In that case there is an ambiguity in its definition which is captured by a scalar function $Q$. We analyze properties of the MST for different choices of $Q$. In doing so, we are led to a definition of "asymptotically Kerr-de Sitter-like spacetimes", which we also characterize in terms of their asymptotic data on $\mathcal{J}^-$.