Too Many Kooks Spoil the Brothel wrote:
The collapse of matter towards the formation of a black hole should
slow down indefinitely, observed "from outside", as it comes nearer and
nearer to forming a horizon. Given the finite age of the Universe, I
cannot see how any could by now have formed. ...

The question (whether a black hole can form in finite external time)
does not have a well-defined answer. Even in special relativity,
simultaneity is relative, and your question is equivalent to: Is there
any time for an external observer that is simultaneous with the time
the black hole forms?

However some other related questions have absolute answers. Given two
events, A and B, we can answer the following questions:

1. Can a signal be transmitted from A to B? (Note that the signal
cannot travel faster than light or backwards in time.)

2. Can a signal be transmitted from B to A?

If #1 applies, we say that A is in the causal past of B. If #2
applies, A is in the causal future of B. It is also possible that
neither is true, i.e., that there is not enough time for a signal to
pass either way. If this is the case, whether A precedes B or vice
versa depends on the choice of reference frame.

Let's take the time a black hole forms to be the time the event horizon
comes into existence. Since not even light can escape from the event
horizon, the black hole's formation is not in the causal past of any
external observer. However, for any such observer, there comes a time
when the black hole's formation is no longer in their causal future.

So do black holes exist yet, or are there only frozen stars? Pick
whatever answer pleases you, and unless someone finds a way to travel
(or communicate) faster than light, no one will ever prove you wrong.

-- Jim Black