Apparent horizon

In general relativity, an apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards, and those directed outward but moving inward.

Apparent horizons are not invariant properties of a spacetime, and in particular they are distinct from event horizons. Within an apparent horizon, light is not moving away from the black hole, whereas in an event horizon, light cannot escape from the black hole. It is possible for light to be currently moving away from the black hole (and so outside the apparent horizon), but in the future will not be able to escape (e.g. because the mass of the black hole is growing) and therefore inside the event horizon. Thus the apparent horizon can be thought of as the boundary of black hole for light at this instant, whereas the event horizon is the boundary of the black hole for light in the future.

The notion of a horizon in general relativity is subtle, and depends on fine distinctions.

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.

Consider 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.

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