1 research outputs found
Uniqueness theorems for static spacetimes containing marginally outer trapped surfaces
Marginally outer trapped surfaces are widely considered as the best
quasi-local replacements for event horizons of black holes in General
Relativity. However, this equivalence is far from being proved, even in
stationary and static situations. In this paper we study an important aspect of
this equivalence, namely whether classic uniqueness theorems of static black
holes can be extended to static spacetimes containing weakly outer trapped
surfaces or not. Our main theorem states that, under reasonable hypotheses, a
static spacetime satisfying the null energy condition and containing an
asymptotically flat initial data set, possibly with boundary, which possesses a
bounding weakly outer trapped surface is a unique spacetime. A related result
to this theorem was given in arXiv:0711.1299, where we proved that no bounding
weakly outer trapped surface can penetrate into the exterior region of the
initial data where the static Killing vector is timelike. In this paper, we
also fill some gaps in arXiv:0711.1299 and extend this confinement result to
initial data sets with boundary.Comment: 30 pages, 9 figure