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As far as I know, as an object gets closer to an event horizon, gravitation time dilation makes it move slower from an outside perspective, so that it looks like it take an infinite amount of time for the object to reach the event horizon. It seems like a similar process should slow the formation of the black hole itself: As the star collapses, its gravitational time dilation makes itself collapse more slowly.

This makes me wonder: from a perspective of an outside observer, can a singularity ever form?

E.g. someone on earth observers a massive star collapse, forming a black hole. From his perspective, the mass gets closer and closer, but does it ever form a singularity before the black hole evaporates?

Furthermore, if from the perspective of a mass collapsing into a black hole, its time slows down and the outside universe "speeds up", could this mean that the black hole evaporates before me, the mass, can become singularity?

UPDATE: Let me show you my reasoning and correct me when I'm wrong (I assume I will be at some point): From a far away observer the black hole forms. Over a very long period it evaporates. In the end, it evaporates down to nothing. According to this link, the black hole cease to exist, the potential singularity is no more.

Now, from a perspective of a massive star: I begin to collapse. All the mass gravitates towards my center. Meanwhile, due to gravitational time dilation from GR, my time ticks slower relative to the rest of the universe. My size crosses the Schwarzschild radius, an Event Horizon is now present. However, now I start to lose mass due to Hawking Radiation. From an outsiders point of view, this is very slow, but from my point of view this is getting faster and faster. Could the singularity form before Black Hole's mass is evaporated?

Qmechanic
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Mateusz Krzaczek
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  • I realize similar questions has been asked before, but they never asked about the perspective of an outside observer, or they were never fully answered about that regard. – Mateusz Krzaczek Apr 28 '21 at 09:51
  • NOTE: I especially care about the singularity itself, not about an event horizon. – Mateusz Krzaczek Apr 28 '21 at 09:52
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    This has definitely been asked before, especially from the perspective of outside observers. See https://physics.stackexchange.com/q/480971/ https://physics.stackexchange.com/q/168095/ https://physics.stackexchange.com/q/5031/ – Eletie Apr 28 '21 at 09:59
  • @Eletie I've read those two questions, all the answers and more questions here and in other sources. Most of the question and answer gravitates (sorry for the unintentional pun) around misunderstanding of time relativity, formation of singularities without EH etc. To me, none of the answers have fully answered my question. – Mateusz Krzaczek Apr 28 '21 at 11:53
  • Few answers that adress MY question directly seems to say.. no? https://physics.stackexchange.com/a/8490/297639 https://physics.stackexchange.com/a/424256/297639 Which is somehow contradicting to other responses that say, from a star perspective, the singularity WILL be formed. – Mateusz Krzaczek Apr 28 '21 at 12:01
  • From another question, that is the closes question to mine I have found, this answer https://physics.stackexchange.com/a/21331/297639 seems to say, again, no. No singularity can ever be formed from a collapsing star. A collapsing mass can come close to it, but from a technical point of view there is no singularity. Those answers seems to be in contradiction to general knowledge that 'we have no idea what happens at singularity', since there are no singularities in the first place. – Mateusz Krzaczek Apr 28 '21 at 12:13
  • What level of familiarity d'you have with GR? Also, I don't see much contradiction with the different answers, the only confusion seems to be about 'whose' frame physically matters. In classical GR, the answer is of course that one needs to study the whole spacetime. This definitively says singularities do form (in finite time), and an infalling observer would hit it too. Questions involving asking 'what's happening now' for an external observer just don't make sense, as there's no correct way to uniquely define simultaneity. It's like asking which spacelike separated event happened first. – Eletie Apr 28 '21 at 12:46
  • @MateuszKrzaczek Are you asking about cosmic censorship (the conjecture that singularities cannot form without an event horizon)? If the singularity forms behind an event horizon, then no outside observer can ever see it form -- by definition of "event horizon." – Chiral Anomaly Apr 28 '21 at 12:49
  • Also, all questions about whether outside observers will see the singularity don't make sense because of the nature of the horizon itself. – Eletie Apr 28 '21 at 12:49
  • @Eletie thank you for your input. I'm not talking about cosmic censorship. Please read the "UPDATE" section of my post that I have just added. In a nutshell: "This definitively says singularities do form (in finite time), and an infalling observer would hit it too." Does this take into account Hawking Radiation and a finite lifespan of a black hole? Wouldn't the mass of a black hole be evaporated before it can form a singularity? – Mateusz Krzaczek Apr 28 '21 at 13:13
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    Yes, even for evaporating black holes the conclusion would be the same. If you study the Penrose diagrams for collapse + evaporation you can see this too. – Eletie Apr 28 '21 at 13:25

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