Global and uniqueness properties of stationary and static spacetimes with outer trapped surfaces

Abstract

Global properties of maximal future Cauchy developments of stationary, m-dimensional asymptotically flat initial data with an outer trapped boundary are analyzed. We prove that, whenever the matter model is well posed and satisfies the null energy condition, the future Cauchy development of the data is a black hole spacetime. More specifically, we show that the future Killing development of the exterior of a sufficiently large sphere in the initial data set can be isometrically embedded in the maximal Cauchy development of the data. In the static setting we prove, by working directly on the initial data set, that all Killing prehorizons are embedded whenever the initial data set has an outer trapped boundary and satisfies the null energy condition. By combining both results we prove a uniqueness theorem for static initial data sets with outer trapped boundary.

38 pages, 2 figures, Latex

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Cited by in corpus (7)

• Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
• Static potentials on asymptotically flat manifolds
• Variational and rigidity properties of static potentials
• A classification theorem for static vacuum black holes. Part I: the study of the lapse
• A classification theorem for static vacuum black holes. Part II: the study of the asymptotic
• A spacetime characterization of the Kerr-NUT-(A)de Sitter and related metrics
• A functional inequality on the boundary of static manifolds