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There are many questions on this forum about objects falling into black holes. Most of them describe that to distant observers, the objects never quite reach the event horizons and appear to be frozen just outside. For example: How can anything ever fall into a black hole as seen from an outside observer?

Answers often refer to the Schwarzchild metric, even though that describes a static situation which isn't strictly applicable to in-falling objects. We know from studies of black-hole mergers (Revisiting Event Horizon Finders ) that in more realistic scenarios, event horizons can start growing before objects actually cross them.

This seems to suggest (perhaps naively) that outside observers could possibly see objects disappear behind event horizons in a finite time, since the event horizon may be larger than previously assumed.

That view might be countered by noting that the gravitational time dilation would also be changing along with the event horizon, with the result that the disappearance would still take an infinite time.

I don't expect that such a complicated situation could have a definitive answer without resorting to numerical relativity calculations, but would like to know what conclusions have been reached about the effects of event horizon growth.

It has been suggested in comments, that this question is a possible duplicate of Does an expanding event horizon “swallow” nearby objects? However, that question involves the merger of two black holes, and therefore has two event horizons, while this question is for the somewhat simpler case of aa object falling into a single black hole. I'm not sure if the answers would be different, but I believe this is still a separate question.

D. Halsey
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In relativity one needs to make a distinction between “an outside event happening at a time $t$ by the clock of an observer $\beta$” and “an observer $\beta$ sees an event happening at time $t$ by her clock”. The first situation means that event happens within the slice of a constant time $t$ in the observer's frame of reference, while the second implies that there is a null geodesics connecting the event with the observer at time $t$.

With that in mind,

  • By taking the backreaction into consideration (in this situation it means that the horizon would be growing) an object would cross the event horizon in finite time by the clock of an outside observer (with any reasonable scheme of defining slices of constant outside time in the vicinity of black hole, such as Fermi–Walker frames)

  • Signals propagating with the speed of light from the event of “object crosses the event horizon” would by definition never reach an outside observer. Signals from events immediately preceding would reach the outside observer arbitrarily late and extremely redshifted, so in practice an observer would only see an object outside the event horizon for some time until the signals from it get redshifted beyond any possibility of detection.

A.V.S.
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