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This question has been on my mind for quite some time.

I don't really have in-depth knowledge about singularities, but from what I understand they rupture the spacetime and they are hard/impossible to describe in a scientific way, because you are dealing with infiniteley dense objects in an infinitely small point. Somehow it seems reasonable to me to assume, they don't exist to avoid all this trouble.

As I understand it, one way that a singularity forms is by a massive star collapsing to a single point under its own gravity. But that's just how the collapsing star experiences it, right? For the outside world, this never happens because time slows down more and more as seen from the outside.

So the singularity is never finished and hence does not exist. All we see, are objects that are endlessly becoming singularities, so the math is still finite. No more headaches.

What are your thoughts on that?

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    $\begingroup$ This question has been asked many times on this site, but there's no concrete answer as it requires a full theory of quantum gravity (which we don't have). But if you're dealing just with GR classically, yes singularities do exist. As for your comment about the singularity never forming for outside observers, this isn't the case. The math does say that singularities exist and they do form in finite time. $\endgroup$
    – Eletie
    Dec 17 '20 at 21:40
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/24934/2451 , physics.stackexchange.com/q/18981/2451 , physics.stackexchange.com/q/75619/2451 and links therein. $\endgroup$
    – Qmechanic
    Dec 17 '20 at 21:44
  • $\begingroup$ @Eletie Yes, they form in finite time but in their timeframe, not in ours. So in our timeframe no one can say "And that thing there is a singularity". For us it'll always be "And that thing there is becoming a singularity". $\endgroup$
    – Dimples
    Dec 17 '20 at 21:52
  • $\begingroup$ Does this answer your question? Are black holes really singularities? $\endgroup$
    – ohneVal
    Dec 17 '20 at 22:07
  • $\begingroup$ @Dimples no, this isn't really the case. I.e. consider any worldlines entering the horizon, which necessarily are part of the spacetime. Please see the other linked stackexchange links for more details, but an observer who enters the horizon of a black hole formed from gravitational collapse will hit the singularity in finite proper time. So this isn't an issue you can just ignore such as by saying the singularity never forms, as you try to do in your answer. e.g. see physics.stackexchange.com/q/137618. $\endgroup$
    – Eletie
    Dec 17 '20 at 22:31