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This is not a duplicate, my question is not about whether BHs have or don't have a singularity, but my question is whether, because of time dilation, no matter has reached the center and formed a singularity in 13.8 billion years (which might just be a second inside the BH).

I have read these questions:

Can we have a black hole without a singularity?

Can a curvature singularity (i.e. BH), as defined in terms of geodesic incompleteness, actually exist in nature?

Why singularity in a black hole, and not just "very dense"?

In his answer to the first question John Rennie says:

I think there is a semi-plausible way to explain why the matter can't avoid collapsing into a singularity, but don't take this too literally. I've mentioned above that if the escape velocity at the event horizon is the speed of light, the escape velocity inside the event horizon must be faster than light. But all forces, e.g. the electrostatic forces that hold you in shape, propagate at the speed of light. That means inside the event horizon the electrostatic force can't hold matter in shape because it can't propagate outwards fast enough. This also applies to the weak and strong forces, and the end result is that no force is able to resist the inwards fall of the matter into a singularity.

Now I do understand that theoretically a BH should have a singularity and all matter would infall towards the singularity, and because the theoretical escape velocity is greater then the speed of light, no forces can hold against the gravitational pull, and matter will fall into a singularity.

My question is different. What I am saying is that 13.8 billion years have passed outside here in our universe, but this might be just a second inside the BH, because of the difference between the stress-energy of the BH and the outside universe (empty space on larger scale); this difference creates such a huge time dilation, that 13.8 billion years on our clock outside here might be just a second inside the BH.

Now this would mean that, although I do understand that no forces can withstand the pull of gravity inwards forming a singularity, still, matter had not enough time to form a singularity just yet.

What I am saying is that maybe 13.8 billion years was not enough for the matter to fall inwards and reach and form a singularity, maybe no single black holes exist where matter would actually have had time to infall toward and form a singularity.

Question:

Is it possible that 13.8 billion years on our clocks here on Earth was not enough (time inside the BH, maybe just a sec) for matter to infall and reach and form the singularity inside the BHs in the universe?

Chappo Hasn't Forgotten
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Árpád Szendrei
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2 Answers2

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There is no well-defined answer to this question. General relativity doesn't define simultaneity in a way that would allow us to say whether a black hole singularity has formed "now." The closest that GR allows us to come to such a definition is that we can form a Cauchy surface, and two events on that surface are "simultaneous" with respect to that surface. But any spacelike surface (with some technical restrictions that are irrelevant here) can be a Cauchy surface.

In your example, you can have a Cauchy surface A that contains the outside observer's "now" and intersects the singularity, or a Cauchy surface B that is also a "now" surface for that observer but doesn't even intersect the horizon.

In terms of B, the matter hasn't even reached the horizon "yet." In terms of A, the matter has "already" passed through the horizon and gone into the singularity.

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Let me argue on basic facts:

1) it is a fact that general relativity has solutions for mass aggregates that have a singularity. Note : the singularity already is described with a mass macroscopically, so large that it fulfills the equations for a singularity at the center, otherwise it will not have the expected mathematical behavior.

2) there are observations in astronomy that can be fitted with a model of a black hole at the center of galaxies, as is true for our galaxy.

3) There are supernova explosions, and in the remnants the existence of a massive black hole is a hypothesis that fits the observations.

One can agree that it is all about models,and note that all these models have a singularity with a large mass at the end.

There is no astrophysical model of a black hole developing in the manner of nucleosynthesis and star formation. There are models for primordial black holes, but that is another story. The models for black hole formation already have a large mass attached for the singularity.

Thus it does not make sense to talk about :"What I am saying is that maybe 13.8 billion years was not enough for the matter to fall inwards and reach and form a singularity". The mass is already there by the supernova explosion that births in its debris a black hole.

Conversely, that is why everything is not a black hole, black holes do not form from the matter they attract, they may grow and that is all.

anna v
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