hide
Free keywords:
General Relativity and Quantum Cosmology, gr-qc,Mathematics, Differential Geometry, math.DG
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.
