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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