Is the growth of black holes paradoxical?

[PeterDonis]

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.)

Not really. The distant observer can't see the horizon at all; light emitted outward at the horizon stays at the horizon. So the distant observer can't see the horizon "move" either.

Here's a way to illustrate what's going on. Suppose there are *three* astronauts. One, astronaut A, free-falls into the hole when it's at its original mass (with a smaller horizon). The second, astronaut B, is hovering at a radius halfway between the old (smaller) and the new (larger) horizon radius; the third, astronaut C, free-falls into the hole after it's reached its new mass (with a larger horizon). Then the distant observer will see all three astronauts' light signals get more and more redshifted and take longer and longer to get to him. But he will see this happen first to astronaut A, then to astronaut B, and finally to astronaut C.

 

[Lino]

Much appreciated Peter.

Regards,

Noel.