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

Abstract

We investigate solutions $(\mathcal{M}, g)$ to Einstein's vacuum field equations with positive cosmological constant $Λ$ which admit a smooth past null infinity $\mathcal{J}^-$ à 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 $\mathcal{J}^-$.

49 pages. v2: Revised version with some changes with respect to the published paper in order to amend a mistake in the statements of theorems 4 and 6 in arXiv:1307.5018v2 (corrected in v3). The validity of all results remains unaltered