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Since I am more confused by the answers given in this site to the many variants and duplicates of this question, with some arguing that from the point of view of the falling observer, it happens in finite time, and the issue is a matter of GR frame of reference (in Can black holes form in a finite amount of time?) and others saying that everything falling into a black hole will always asymptotically falls towards the event horizon, but never actually crossing it (in How can anything ever fall into a black hole as seen from an outside observer?), I am going to pose this question as a thought experiment, hoping that I will be able to make sense out of the answer, and get to a conclusion myself:

Imagine I am standing on altitude $h$ above a non-rotating black hole of mass $M$. I am not in orbit, but I am not falling because I am in a rocket that perfectly counters the gravity, keeping me stationary. I have with me a magic ball. It is magic because it can fly like Superman, thrusting with any finite amount of force. So, no matter how close it gets to the event horizon, as long as it doesn't crosses it, it can escape flying radially outwards. Now I drop my ball from the rocket that free falls radially into the black hole. It can decide at any moment to use its powers to try to climb up back to the rocket, but I don't know when or if that will happen.

So, how much time I must wait to be completely sure that my ball crossed the event horizon and will never return?

Since I am more confused by the answers given in this site to the many variants and duplicates of this question, with some arguing that from the point of view of the falling observer, it happens in finite time, and the issue is a matter of GR frame of reference (in Can black holes form in a finite amount of time?) and others saying that everything falling into a black hole will always asymptotically falls towards the event horizon, but never actually crossing it (in How can anything ever fall into a black hole as seen from an outside observer?), I am going to pose this question as a thought experiment, hoping that I will be able to make sense out of the answer, and get to a conclusion myself:

Imagine I am standing on altitude $h$ above a non-rotating black hole of mass $M$. I am not in orbit, but I am not falling because I am in a rocket that perfectly counters the gravity, keeping me stationary. I have with me a magic ball. It is magic because it can fly like Superman, thrusting with any finite amount of force. So, no matter how close it gets to the event horizon, as long as it doesn't crosses it, it can escape flying radially outwards. Now I drop my ball from the rocket, and it free falls radially into the black hole. It can decide at any moment to use its powers to try to climb up back to the rocket, but I don't know when or if that will happen.

So, how much time I must wait to be completely sure that my ball crossed the event horizon and will never return?

Since I am more confused by the answers given in this site to the many variants and duplicates of this question, with some arguing that from the point of view of the falling observer, it happens in finite time, and the issue is a matter of GR frame of reference (in here Can black holes form in a finite amount of time?) and others saying that everything falling into a black hole will always asymptotically falls towards the event horizon, but never actually crossing it (in here How can anything ever fall into a black hole as seen from an outside observer?), I am going to pose this question as a thought experiment, hoping that I will be able to make sense out of the answer, and get to a conclusion myself:

Imagine I am standing on altitude $h$ above a non-rotating black hole of mass $M$. I am not in orbit, but I am not falling because I am in a rocket that perfectly counters the gravity, keeping me stationary. I have with me a magic ball. It is magic because it can fly like Superman, thrusting with any finite amount of force. So, no matter how close it gets to the event horizon, as long as it doesn't crosses it, it can escape flying radially outwards. Now I drop my ball from the rocket that free falls radially into the black hole. It can decide at any moment to use its powers to try to climb up back to the rocket, but I don't know when or if that will happen.

So, how much time I must wait to be completely sure that my ball crossed the event horizon and will never return?

Since I am more confused by the answers given in this site to the many variants and duplicates of this question, with some arguing that from the point of view of the falling observer, it happens in finite time, and the issue is a matter of GR frame of reference (in Can black holes form in a finite amount of time?) and others saying that everything falling into a black hole will always asymptotically falls towards the event horizon, but never actually crossing it (in How can anything ever fall into a black hole as seen from an outside observer?), I am going to pose this question as a thought experiment, hoping that I will be able to make sense out of the answer, and get to a conclusion myself:

Imagine I am standing on altitude $h$ above a non-rotating black hole of mass $M$. I am not in orbit, but I am not falling because I am in a rocket that perfectly counters the gravity, keeping me stationary. I have with me a magic ball. It is magic because it can fly like Superman, thrusting with any finite amount of force. So, no matter how close it gets to the event horizon, as long as it doesn't crosses it, it can escape flying radially outwards. Now I drop my ball from the rocket that free falls radially into the black hole. It can decide at any moment to use its powers to try to climb up back to the rocket, but I don't know when or if that will happen.

So, how much time I must wait to be completely sure that my ball crossed the event horizon and will never return?