Communications in Mathematical Physics

, Volume 322, Issue 2, pp 633–666 | Cite as

Global and Uniqueness Properties of Stationary and Static Spacetimes with Outer Trapped Surfaces

  • Marc MarsEmail author
  • Martin Reiris


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.


Black Hole Initial Data Killing Vector Smooth Point Cauchy Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Facultad de CienciasUniversidad de SalamancaSalamancaSpain
  2. 2.Albert Einstein InstitutMax Planck Institut für GravitationsphysikPotsdamGermany

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