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I have read this question:

The simple answer is that no, the Big Bang did not happen at a point. Instead, it happened everywhere in the universe at the same time. Consequences of this include

  • The universe doesn't have a centre: the Big Bang didn't happen at a point so there is no central point in the universe that it is expanding from.
  • The universe isn't expanding into anything: because the universe isn't expanding like a ball of fire, there is no space outside the universe that it is expanding into.

Did the Big Bang happen at a point?

Now this has been puzzling me for a while, does the singularity of a black hole happen at a point, or does it happen everywhere at the same time:

  • The black hole does not have a centre: the singularity does not happen at a point, so there is no central point in the black hole

  • the black hole isn't squeezing into anything: because the black hole isn't squeezing like a ball of fire, there is no space that it would be squeezing into

Now on this site, many draw similarities between the singularity of the big bang, and the singularity of a black hole, in that the initial singularity (big bang) was the start from where space expanded, and in the case of a black hole space contracts into a singularity. Now if the big bang did not happen at a point, but happened everywhere at the same time, then does the contraction of space in a black hole happen (does the singularity "happen") everywhere at the same time?

Question:

  1. We say the big bang (initial singularity) didn't happen at a point, but is it the same with the singularity of a black hole?
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    $\begingroup$ According to the current cosmology, we live be in the “observable universe” and whether anything beyond it even exists makes no difference to us. The Big Bang did happen at a point for the “observable universe” and it does have a center. $\endgroup$
    – safesphere
    Commented Oct 20, 2022 at 7:05
  • $\begingroup$ In Figure 1 at nobelprize.org/uploads/2020/10/advanced-physicsprize2020.pdf , in connection with the award of a Nobel Prize in physics to Roger Penrose, the Nobel Prize Committee itself has represented the black hole singularity as a small dot centered on the center of a black hole. Connecting this to the question of whether "the universe" started at a point would rely on a "black hole genesis" model: Although BHG originated with Lee Smolin, the cosmological model most often associated with it may be Nikodem Poplawski's, but it relies on Einstein-Cartan Theory, not GR. $\endgroup$
    – Edouard
    Commented Oct 21, 2022 at 18:20
  • $\begingroup$ The OP may have included only a General Relativity tag because PSE currently lacks any tag for ECT; also, ECT (developed in conversations between Einstein and the mathematician Cartan in 1929) is said to "reduce to GR" in vacuum, which would be consistent with the "universe from nothing" of inflationary models (such as Poplawski's), in which the interior space of local universes (but not of the entire cosmos) would expand at a quasi-exponential rate. $\endgroup$
    – Edouard
    Commented Oct 21, 2022 at 18:51

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Not exactly. In this answer, I'll deal mainly with Schwarzschild black holes, which are a bit simpler. I'll comment on more general black holes at the end, but I'll leave for someone else to cover the details.

Schwarzschild Black Holes

Both the Big Bang and black hole singularities (reminder: I'm assuming a Schwarzschild black hole for now) are spacelike singularities. This means essentially that they do not happen at a place, but at a time. However, they are still considerably different.

All observers arose from the Big Bang. Hence, in this sense, it did happen everywhere at once. You will never find an observer (i.e., a path through spacetime) which did not start at the Big Bang.

Black holes, on the other hand, are a bit different. You will find observers who will never fall into a black hole, and hence will never hit the singularity inside it. In this sense, the singularity is not everywhere, because not every observer will crash into it. It is possible, for example, for observers to go to infinity in infinite time.

Hence, it is correct to say the singularity at a black hole doesn't happen at a (spatial) point. It is never "to the right" of an observer, for example. It is to the future. However, there are also some differences when we compare it with the Big Bang, so, at least in my opinion, it is not fair to say the singularity happens everywhere (it happens inside the black hole).

Charged and Rotating Black Holes

For Reissner–Nordstrom (charged) and Kerr (rotating) black holes (or for the more general Kerr–Newman (charged and rotating) black holes), the singularity is not spacelike. In fact, you end up with a fair more complicated structure inside the black hole, and there is the possibility of an observer simply navigating through the black hole without ever hitting the singularity (this is impossible in Schwarzschild, in which every observer that enters the black hole hits the singularity in finite time). Hence, this situation is way more different from the Big Bang singularity, and the singularities do happen at a place, not an instant. PBS Spacetime discussed a bit of the Kerr structure in the episode Mapping the Multiverse, in case you're interested.

It is worth recalling that these solutions assume high levels of symmetry and might not reflect what actually happens after stellar collapse. In real situations, the singularities might be fairly different.

Edit: as pointed out by safesphere in the comments, spinning a Schwarzschild black hole will lead to the singularity becoming a ring-like structure. This time, it is unavoidable to cross a structure known as the Cauchy horizon, which is a null (lightlike) surface within the black hole. Since it is unavoidable for anything that fell inside the black hole, the Cauchy horizon happens everywhere within the Kerr black hole in the same sense the Schwarzschild singularity happens everywhere within the Schwarzschild black hole. A similar comment also holds for Reissner–Nordstrom black holes, although the singularity is not ring-like.

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    $\begingroup$ This is less reliable, so I'll leave it to the comments: I heard a while ago that there were some results suggesting stellar collapse would lead to null singularities instead of timelike singularities in Kerr and RN black holes, which would then end the "infinite tower" structure. In this case, it would resemble a bit more my Schwarzschild answer. However, I don't know a reference and I haven't checked much for it, so take this bit with a grain of salt $\endgroup$ Commented Oct 17, 2022 at 22:41
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    $\begingroup$ Would it be fair to say that the Schwarzchild singularity happens everywhere within the entire horizon? $\endgroup$
    – rob
    Commented Oct 18, 2022 at 0:07
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    $\begingroup$ @rob Since every observer/light ray that crosses the event horizon will reach the singularity in finite time, I think that's perfectly fair. I'm assuming we're not counting the event horizon itself, only its interior. As far as I remember a light ray can stay moving along the event horizon forever without falling into the singularity $\endgroup$ Commented Oct 18, 2022 at 0:55
  • $\begingroup$ @NíckolasAlves Are you mixing up the event horizon with the “photon sphere”? My hand-waving understanding is that the event horizon is where the cone of photon trajectories which escape collapses to zero solid angle. $\endgroup$
    – rob
    Commented Oct 18, 2022 at 2:57
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    $\begingroup$ @rob I agree with safesphere. My point with the photons on the horizon is not that their orbits are stable (they certainly are not, since slight deviations towards the interior will lead to the singularity), but rather that the horizon is a congruence of null geodesics, i.e., it is formed by "light rays". In an unphysically perfect situation, a light ray could remain exactly on the event horizon forever without ever reaching the singularity. In practice, those are indeed unstable orbits $\endgroup$ Commented Oct 18, 2022 at 18:07

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