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Caption: Apparent Versus Absolute Horizon
Event Horizon Growing
Consider a star that will eventually collapse to a black hole. Initially,
when it begins to collapse light rays are only slightly affected by its
gravity. As the collapse continues and the density increases, an event
horizon may form. The event horizon is a special surface traced out by
light rays that will never escape to infinity away from the star, and will
never fall back in. But in a dynamic system like a collapsing star, the
event horizon is usually expanding out! As more matter falls in, the
expansion of the event horizon slows down as the mass inside it, and hence
the gravitational pull on the light rays, increases. This process is
depicted in the first picture: the event horizon is expanding, although
it will eventually stop expanding when all the matter has fallen inside.
Apparent Horizon Forms
During the collapse there may be a surface of "outgoing" light rays (i.e.,
light rays that are directed away from the star, not towards it) that at
some moment is not expanding due to the pull of gravity inside. This
surface may even be contracting! This is called a trapped surface. If
that surface is neither expanding nor contracting (i.e., it has zero
expansion), but is just balanced against the pull of gravity, it is called
an apparent horizon. Such a surface is shown in the second picture, and
if it exists it cannot be outside the event horizon.
Both Horizons Coincide
Apparent horizons are convenient in numerical relativity because one only has to test the
surface at some instant in time to see if it has no expansion. On the
other hand, the event horizon is generally expanding: only at the very
end of the dynamical process will it cease to expand. At this point, the
event horizon and the apparent horizon will coincide, as depicted in the
final picture.
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NCSA. Last modified 11/7/95