Apparent Horizon - Definition

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.

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