How does an absolute horizon form before the apparent horizon?

Question

If I understand it correctly, the apparent horizon is the boundary between where light directed outwards will move outwards, and light directed outwards will move inwards. Even if light is moving away from the black hole outside of the apparent horizon, it will not escape to infinity if it is within the event horizon.

The event horizon is essentially the apparent horizon in the future, if the apparent horizon continues growing. Theoretically, the two horizons should eventually meet up...again, if I understand it correctly.

My confusion is with how the two form. According to Wikipedia,

In the simple picture of stellar collapse leading to formation of a black hole, an event horizon forms before an apparent horizon.

My main question is, how can the event horizon form "before" the apparent horizon? I understand that one can slice the Schwarzschild geometry so that there is no apparent horizon at all, but if an apparent horizon exists, I still don't understand how or why it would form after the event horizon.

Answer 1

I guess you are talking about black hole formation here. If we take the Oppenheimer-Snyder model for the spherically symmetric collapse of a star, then an event horizon forms first followed later by an apparent horizon that is at, or interior to, the event horizon.

The event horizon is the surface behind which light rays will never reach an infinite distance from the black hole. The apparent horizon is the surface behind which outwardly directed light rays will move inward.

The two will coincide for a static black hole, but for a forming black hole with a growing mass, it is possible for an outwardly directed photon to be outside the apparent horizon, but inside the event horizon, because the black hole mass is inevitably larger in the future if some of its future mass is still beyond its final Schwarzschild radius. As the event horizon forms at the centre of the star and moves outwards, then it is clear that the apparent horizon, which is always interior to the event horizon, must form later.

In the very simplified Oppenheimer-Snyder model, featuring an initially uniform star comprising of pressureless "dust", the apparent horizon first forms just as the surface of the collapsing star coincides with the event horizon and the apparent horizon is therefore always coincident with the event horizon. In more realistic models the apparent horizon forms a little earlier and then moves outwards to coincide with the event horizon as the surface of the collapsing star moves inside the event horizon.

NB: Note that whilst the apparent horizon can be defined at any point in time, the "event horizon" referred to above is a theoretical ideal, since we cannot preclude that the black hole might accrete some more mass in the future!