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

Abstract

We investigate solutions(M, g) to Einstein's vacuum field equations with positive cosmological constant. which admit a smooth past null infinity 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 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 J(-).