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This is a kind of follow-up of my previous Phys.SE question Can something (again) ever fall through the event horizon? that seems to have established that, for an outside observer, things never fall into the black hole. Note that this is not to say that an outside observer never sees anything falling into a black hole (as in receiving the optical signal), but it is instead an stronger statement: no matter how long an outside observer wait for anything to fall into a black hole, there will always exist intersection between his own future light cone and the in-falling object's light cone outside the event horizon. That is what I mean by "things never fall into the black hole".

Assume an initial universe with no black holes (stellar or primordials), and thus, has no event horizons. Is there a solution to GR equations showing that the light cone of any amount of mass will inevitably reach a singularity, never intersecting with the light cone of an observer outside the would-be-black-hole? For my understanding, the Schwazschild metric describes an eternal, static, black hole, so I guess I am looking for something else here.

Please notice that I tried to be much more specific than the other questions about black hole formation, because the answers saying that in falling observers would reach the singularity in a finite amount of proper time isn't really helping me to understand the phenomenon from an outside perspective.

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    $\begingroup$ Good question. You might get some trivial answers, and some great ones. I don't have an answer, but do have a way of thinking it. Just like the two black holes that were observed merging in 2015 (we 'saw' them and it didn't take them an infinite amount of time) other black holes form in a reasonable time, even for an observer at infinity. The infalling matter gets close enough to the horizon, maybe within a few Compton wavelengths or less, that for all practical purposes you can consider them have been absorbed in.You can treat them (except for quantum distances) like they did form the horizon $\endgroup$
    – Bob Bee
    Apr 8, 2017 at 21:18
  • $\begingroup$ So, what I want to know is if the astronomical objects we see as black holes are really the black holes in the solution of GR equations, or one is just a really good approximation of the other. If the astronomical black hole is just a very heavy compact object that distorts time asymptotically to a halt, but never really forms an event horizon, then, for all external practical purposes, it is a black hole, but manages to avoids all the Schwarschild solution's singularities and bizzarities. $\endgroup$
    – lvella
    Apr 8, 2017 at 22:09
  • $\begingroup$ I am pretty sure you can form a Schwarzschild black hole from a spherically symmetric collapse of a star, although you can say that such a process is unphysical as well. $\endgroup$
    – John
    Apr 8, 2017 at 22:22
  • $\begingroup$ The light cone of a particle is clearly defined on the particle. In general, a particle is moving in spacetime. When you say the 'light cone of any amount of mass will inevitably reach a singularity', do you mean 'any amount of mass will inevitably reach a singularity'? $\endgroup$
    – John
    Apr 8, 2017 at 22:30
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    $\begingroup$ Also see physics.stackexchange.com/questions/1916/… $\endgroup$
    – ProfRob
    Apr 9, 2017 at 11:51

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I can't claim I have an answer but I will aim to clarify some points.

If you have no black holes to begin with, it is not necessary that you form a black hole. Therefore, a quick answer is no - if there are no singularities to begin with and no singularities are subsequently formed, then obviously nothing will ever hit a singularity.

However, if you take Schwarzschild and put some mass at rest in Schwarzshild, then they will definitely fall into the black hole and hit the singularity. As you pointed out, an outside observer wouldn't see that. Personally, I think it would be very weird just seeing an object disappearing. The picture of "things never fall into the black hole" is much more natural.

You might be looking for a naked singularity (without an event horizon). A naked singularity is believed not to exist generically, and is related to the Weak Cosmic Censorship Conjecture. You can certainly come up mathematically with spacetimes that contain naked singularities. In those cases, it might be true that things can just disappear.

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  • $\begingroup$ "then obviously nothing will ever hit a singularity" Well, that is why I phrased it that way, because I wanted to know if a black hole could form. "I think it would be very weird just seeing an object disappearing" That is precisely what happens, even in astronomical black holes (that might actually be just approximated by GM black hole solutions), because its light is redshifted into oblivion pretty quickly. $\endgroup$
    – lvella
    Apr 10, 2017 at 1:29
  • $\begingroup$ Lastly, an object will not "definitely fall into the black hole and hit the singularity" from an outside frame of reference, only from frame of references that eventually crosses the event horizon. I guess I was not clear enough when I gave my definition of "never falling" in terms of light cone. My "never" there was in some frame of reference in the outside universe. There, no finite amount of time is enough for the object to definitely cross (see the question I've linked). $\endgroup$
    – lvella
    Apr 10, 2017 at 1:37
  • $\begingroup$ I think you are misinterpreting what I meant - I meant when something falls into the BH, it would be weird to see it just disappears as you see it crosses the event horizon! What we know is that, from our perspective, the object will take infinite time to cross the event horizon. I don't understand why you are making a fuss about whether it crosses from an outsider's perspective either. Just use the infalling object's proper time to parametrise and you find that it does cross the event horizon like it wasn't there. As I mentioned, the lack of an event horizon is believed to be unstable. $\endgroup$
    – John
    Apr 10, 2017 at 20:49
  • $\begingroup$ As for your first question: Black holes could certainly form even if you started out with no black holes, e.g. from collapse of stars. And for astronomical black holes: you don't see them disappear. Nobody has witnessed disappearing of a star to form a black hole. $\endgroup$
    – John
    Apr 10, 2017 at 21:03
  • $\begingroup$ I haven't claimed that black holes disappear, you've misinterpreted me. What disappears is the in falling object, because any light the object might emmit is redshifted to undetectable wavelengths. So, an in falling object would indeed seem to disappear for an external observer, as its light becomes undetectable. No eye or telescope can see an object that is close enough to a black hole. $\endgroup$
    – lvella
    Apr 10, 2017 at 21:39

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