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Outer Apparent Horizon is a Null Hypersurface
Let $(N,h)$ be a 4 dimensional spacetime, $M$ be some spacelike hypersurface in $N$ and $S$ be some closed hypersurface in $M$. Let $K$ be some null normal field on $S$. This is the standard set up ...
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Definition of trapped surface
The definition of a trapped surface in Sean Carroll's "Spacetime and Geometry" is as follows.
"A compact spacelike, two dimensional submanifold with the property that outgoing future directed light ...
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