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 $\Lambda$ 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

References in corpus (2)

• On the uniqueness of smooth, stationary black holes in vacuum
• Symmetric hyperbolic systems for a large class of fields in arbitrary dimension

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