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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?

Qmechanic
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Dimples
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    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. – Eletie Dec 17 '20 at 21:40
  • Possible duplicates: https://physics.stackexchange.com/q/24934/2451 , https://physics.stackexchange.com/q/18981/2451 , https://physics.stackexchange.com/q/75619/2451 and links therein. – Qmechanic Dec 17 '20 at 21:44
  • @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". – Dimples Dec 17 '20 at 21:52
  • Does this answer your question? Are black holes really singularities? – ohneVal Dec 17 '20 at 22:07
  • @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 https://physics.stackexchange.com/q/137618/. – Eletie Dec 17 '20 at 22:31
  • "Singularity" is a very general mathematical term. The question seems to be dealing with a particular area of physics - I suggest outlining the context more clearly. – Roger V. Dec 18 '20 at 02:18
  • Does this answer your question? Can black holes form in a finite amount of time? – John Rennie Dec 18 '20 at 09:45
  • @Eletie I think we are getting closer. In your refered link it says So we never actually see the event horizon form and that's what I mean. So in our time, it is never finished and therefore doesn't exist. We can never see a finished singularity unless we jump into one. As seen in proper time from the perspective of the collapsing star, everything happens without slowing down but as we approach the event horizon, doesn't the universe collapse around us because it is now infinitley old? – Dimples Dec 18 '20 at 15:52
  • @Eletie That also means, that no one can say, "In that constallation over there is a black hole and in its center is a singularity" because it is still in the process of forming and it is not finished – Dimples Dec 18 '20 at 16:01
  • @Dimples The point is that the notion of black holes, event horizons and singularities are necessarily global phenomena. Moreover, if a singularity exists in the spacetime and even your future lightcone, you can't pretend it's not there because a) you don't see outgoing photons from it and b) deciding that you as an observer won't travel there. You also seem to be confusing the issue of simultaneity in relativity. It doesn't make sense something doesn't exist just because you can't observe it along a specific worldline. You need to consider all worldlines. – Eletie Dec 18 '20 at 17:01
  • @Dimples Imagine you observe me falling into a black hole. You can go on pretending that I'm still alive and fine, hanging out infinitesimally close at the horizon (ignoring the fact you eventually see my photons redshift and then stop), but what does it mean to say 'they're not in the black hole! They're fine, just outside the horizon!'. My wordline passes through the horizon and hits the singularity in finite proper time, this is what's important. When talking about spacetime in GR we need to consider the whole spacetime and all trajectories. I.e. what happens to geodesics. – Eletie Dec 18 '20 at 17:03
  • The Oppenheimer Snyder metric is produced from collapsing dust and has a region of spacetime which is identical to the corresponding region of the Schwarzschild metric. This identical region includes part of the Schwarzschild singularity. So it is not specifically a Schwarzschild singularity, but it is a singularity. Also, as Penrose famously showed such results are “a robust prediction of the general theory of relativity” – Dale Dec 18 '20 at 23:42
  • @Eletie Thanks for your clarification. 1. So, in my wordline you never reach the black hole and a collapsing star will never form a singularity, right? That's what I mean by no one can say, "In that constallation over there is a black hole and in its center is a singularity 2. In your wordline, falling into the black hole, you will be hitting the event horizon in finite time, yes. But in that time, the universe around you has become infinitely old, right? So, who knows if it is still there to contain your black hole and follow the laws of phsyics as we know them? – Dimples Dec 21 '20 at 13:56
  • @Dimples you may be misunderstanding the concept of worldines: these are paths through spacetime and not just a matter of perspective. In doing spacetime physics we need to consider all the geodesics/physical worldines of that spacetime. And your 2 isn't right, the universe doesn't become infinitely old: the incoming light received by an observer falling into a black hole isn't from the entirety of the future outside the horizon. Looking at the Kruskal series Penrose diagram shows there are no lightlike curves from the future infinity ($i^+$ and $i^0$) to a the singularity at $r=0$. – Eletie Dec 21 '20 at 15:07

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