Definition
The notion of an apparent horizon begins with the notion of a trapped null surface. A (compact, orientable, spacelike) surface always has 2 independent forward-in-time pointing, lightlike, normal directions. For example, a (spacelike) sphere in Minkowski space has lightlike vectors pointing inward and outward along the radial direction. The inward-pointing lightlike normal vectors converge, while the outward-pointing lightlike normal vectors diverge. It can, however, happen that both inward-pointing and outward-pointing lightlike normal vectors converge. In such a case the surface is called trapped.
We can take the set of all such trapped surfaces. In terms of a simple Schwarzschild black hole, these surfaces fill up the black hole. The apparent horizon is then defined as the boundary of these surfaces — essentially, it is the outermost surface of the black hole, in this sense. Note, however, that a black hole is defined with respect to the event horizon, which is not always the same as the apparent horizon.
Any apparent horizon is observer dependent.
Read more about this topic: Apparent Horizon
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