Black hole growth paradox

I'm trying to understand the experience from the distant observers perspective.

I was under the impression that the rate at which the at which the astronaut is seen moving toward the event horizon (and the red shift of his signal) will approach infinity and so never actually (be seen to) cross the event horizon.

But my reading of the previous posts is that from the perspective of the distant observer, irrespective of the astronaut falling-in or the event horizon growing, the astronaut / signals will drop behind the event horizon and disappear.

what I envisaged was that for the free falling astronaut would appear to slowdown / fade but never stop or disappear, but for the expanding event horizon the astronaut would disappear completely.

if the rate at which the horizon expands slows and "freezes" (as it approaches the astronaut)

It doesn't. Light signals emitted outward by the astronaut get more and more redshifted and take longer and longer to get out to the distant observer, but that's not the same as saying the expansion of the horizon itself slows and freezes. The astronaut will find himself at the new horizon in a finite length of time by his own clock; it just takes an infinite amount of time by the distant observer's clock for that information to get out to him.

Now, this led early on to an image of a black hole as a strange sort of suspended-animation object, a "frozen star" with immobilized falling debris and gedankenexperiment astronauts hanging above it in eternally slowing precipitation. This is, however, not what you'd see. The reason is that as things get closer to the event horizon, they also get dimmer. Light from them is redshifted and dimmed, and if one considers that light is actually made up of discrete photons, the time of escape of the last photon is actually finite, and not very large. So things would wink out as they got close, including the dying star, and the name "black hole" is justified.

Much of what people say about the vicinity of black holes doesn't seem to make sense.

For instance, it seems to be impossible for a black hole to grow by "ingestion" by scooping up matter around it or in its path, at least in the traditional sense. Gravitational time dilation takes care of that -- no particle having mass will ever reach the event horizon, much less travel through it, and because of the asymptotic partitioning of space-time at the horizon, I don't think that even a photon can penetrate a black hole as it would have to raise itself to an infinite frequency. So an event horizon seems to be impenetrable -- from either direction.

However, it seems that a black hole can ingest matter by growing. If a massive object approaches a black hole, and comes close enough such that the two combined masses (or portions of a mass) now fit within their paired Schwarzschild radius, a new shell-like event horizon will form behind the intruding mass, and in the process, any other matter around the original black hole is now engulfed within the new expanded radius.

For instance, if a neutron star of about two solar masses approaches a black hole containing about 60 million solar masses such that its entirety is within about 6 kilometers of the event horizon, a new event horizon will form behind it, and in the process engulf enough space to contain the volume of the Sun (if my math is correct).

[..]

Comments please?

Chris

I understand the logic of the astronaut dimming but not why it would “wink out” (I don’t think that he “runs-out” of photons).

Which brings me back to the FAQ quote, maybe both do “wink out”, but why?

I can appreciate that the speed of the expanding event horizon might slow as it approaches its new resting place

Notice that whether the horizon "slows" depends on your choice of coordinates. In a local inertial frame, the horizon expands at c! Even a "static" horizon expands at c from the point of view on an observer who is crossing it.
If you are not familiar with the Rindler horizon, I suggest you have a look at it. It's a simple case, involving no gravity and no spacetime curvature, of an event horizon with many features of a black hole's horizon, including redshift, objects falling past the horizon but never appearing to do so to a distant observer, causally disconnected regions of spacetime etc. It's like the horizon of a very large black hole, with negligible tidal forces. See for example this.

... all the photons he detects would have been emitted by the astronaut from some point above the horizon. ...

... If the distant observer could detect photons of any finite frequency, however low, he would continue to detect them (at lower and lower frequency, and coming further and further apart) forever by his clock ...

I also understand that for the expanding horizon scenario the distant observer could detect photons at lower and lower frequency ... but I would have assumed for a finite period of time.

(I hope that this doesn't add confusion, but it strikes me like a "radioactive half life" problem: in that (for the distant observer) the time for the horizon to move to the new location appears infinite, but the time taken for the horizon to reach half way (i.e. the location of the astronaut) can be measured specifically.)