So, one has to take the causal structure of spacetime into consideration. Good insight, thanks for clarifying.This statement: "event horizon of the collapsing star is formed in the infinite future "
is not accurate. Accurate is:
No event at or inside event horizon is ever in the causal past of an eternally external observer.
See the difference? "Not in causal past" is not at all the same as "infinite future". The horizon formation CAN be treated as in the past, present, or future of an external observer (just not the causal past) depending on how they choose to foliate the region of specetime that is neither in their past nor future light cone. Note, in particular, there is a precise moment when the horizon formation is no longer in the future light cone of an external observer. This makes it fair game to be treated as 'now' or even 'past', but not causal past.
WannabeNewton, thanks for your hint.