Local existence of dynamical and trapping horizons

Abstract

Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally outer trapped slices which lie in the leaves of the given foliation. We also show that under rather weak energy conditions this horizon must be either achronal or spacelike everywhere. Furthermore, we discuss the relation between ``bounding'' and ``stability'' properties of marginally outer trapped surfaces.

4 pages, 1 figure, minor changes

References in corpus (4)

• General Laws of Black-Hole Dynamics
• Dynamical Horizons and their Properties
• Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
• Trapped surfaces and symmetries

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