A trapped surface is a closed spacelike codimension-two surface whose two future-directed orthogonal null congruences both have negative expansion.
A closed spacelike two-surface is marginally outer trapped when its future outgoing null expansion is zero. For the future black-hole type, the ingoing null expansion is negative. An apparent horizon on a chosen spatial slice is ordinarily its outermost such surface under suitable regularity assumptions. The notion depends on the slice and is not the global definition of an event horizon.
An apparent horizon is the outer boundary of the future-trapped region on a chosen spatial slice, under the usual regularity conditions. Its location depends on the slice; it is not the globally defined event horizon. At a regular boundary the outward null expansion vanishes while the inward null expansion is negative. Its area cannot be substituted into every version of the Penrose inequality without the appropriate area and initial-data hypotheses.
An anti-trapped surface is the time reverse of a trapped surface: both future-directed orthogonal null expansions are positive.
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A trapped surface is a concept in the field of general relativity, specifically in the study of black holes and gravitational collapse. It refers to a two-dimensional surface in spacetime that has certain properties related to the behavior of light rays. In more technical terms, a trapped surface is defined as a surface such that all light rays emitted orthogonally (perpendicular) to the surface are converging.