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How can a star that turns into a black hole technically be smaller than a quark? $10^{12}$ atoms $\geq$ 1 quark. That shouldn't work.

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    $\begingroup$ You left out a lot of zeros! $\endgroup$ – G. Smith Oct 28 '19 at 2:20
  • $\begingroup$ According to the Schwarzschild metric, the volume inside the black hole is infinite, so the average density is zero. $\endgroup$ – safesphere Oct 28 '19 at 7:18
  • $\begingroup$ @safesphere : I am not sure how good it is to talk about a "volume inside" the black hole. To talk about volume, i.e. 3-dimensional, we need to be able to have a sensible way to pick a 3-dimensional space-like slice of an object with which to find that - essentially, what the object looks like "now". But in a curved spacetime - esp. the extreme one of a black hole - there is essentially no non-arbitrary notion of "now" at all: no well-defined global simultaneity. In what way is one defining the "volume", then? $\endgroup$ – The_Sympathizer Nov 4 '19 at 8:41
  • $\begingroup$ @The_Sympathizer We can define it as a Schwarzschild time slice. Then the symmetry is preserved and the volume geometry is a hypersurface of a spherindle. To visualize it in the reduced number of dimensions, it is like a surface of a thin cylinder shrinking in radius over time from the Schwarzschild radius to zero. The singularity is the axis of the cylinder not located anywhere in space (surface). So while inside, an observer cannot see or point to a singularity. It does not exist yet (is in the future) at any moment of time inside the BH. See the 3D diagram linked in my comment below. $\endgroup$ – safesphere Nov 4 '19 at 15:49
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For one thing, actually, we don't know if it is possible to "compress matter infinitely". The idea that matter becomes infinitely compressed comes from our best theory - general relativity - of how space and time work: once you compress matter to within a suitably small finite volume, it must continue to compress itself no matter how strong it otherwise would be or how much matter you have, and hence has no alternative but to compress to a size of zero. In effect, space and time distort in such a way that there are no permissible movements anymore except those which serve to push things closer together.

But the trouble is, our other best theory of physics - quantum mechanics - which is the theory of how matter works, doesn't like that (for reasons too complicated to get into here)! It doesn't like the idea of infinitely compressed matter. Hence, either one or both of these has to be wrong, so it may be that matter doesn't "compress infinitely". Or maybe it does - the problem is, we can't know, and those that state this as a "truth" are being sloppy and misleading.

But if you want to nonetheless insist on the idea, then a rather simple intuitive idea for how a zillion atoms could compress themselves into a point, would have to be this. The particles that make up atoms (quarks and electrons) are, themselves, point-sized (quantum has no problem with that; it's with trying to smash a bunch of them together that it starts running into issues - as said, this is an oversimplified, intuitive idea). Thus they already have size zero. Matter, essentially, is entirely empty space, while it's forces that those zero-size particles project onto each other that give it the appearance of shape and extent. Compressing those particles all to a point, then, just means taking away all that empty space between them. A black hole core is matter with no empty space left in it at all. Since a zillion zeros add to zero, a zillion point-size particles add to a single point, and the result is that they all occupy one and the same point.

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  • $\begingroup$ "how a zillion atoms could compress themselves into a point" - The Schwarzschild singularity is not a point. The worldline of the BH center is an infinitely long line $(r=0; -\infty<t<+\infty)$ where $r$ is timelike while $t$ is spacelike. So the singularity is an infinitely long spacelike line that exists for a zero period of time. $\endgroup$ – safesphere Nov 4 '19 at 8:29
  • $\begingroup$ @safesphere : Hmm. However, I'd raise that the analogy is still useful because, for one, you still have the problem of a 3-dimensional object then becoming 1-dimensional and, for another, actually, elementary particles are themselves "lines" too, when you consider their temporal extent given that we are necessarily talking about space-time here and so have to be consistent in the picture we're using. In a sense, the black hole singularity "lives sideways" - its history stretched "horizontally" across space as though it were travelling faster than light - as compared to other objects. $\endgroup$ – The_Sympathizer Nov 4 '19 at 8:39
  • $\begingroup$ I think the key here is that each particle ends up in a different point of the singularity. As an illustration, imagine a handful of sand. Then, instead of trying to squeeze it into a smaller volume, spread it into a one-grain thin line. This way no two particles are squeezed into each other and don't need to have a very high Fermi temperature. Once matter is spread this way, squeezing each particle into a zero volume is not a problem, because particles are poinike anyway, as you stated in the answer. $\endgroup$ – safesphere Nov 4 '19 at 15:20
  • $\begingroup$ "elementary particles are themselves 'lines' too" - Yes, but worldliness of particles are perpendicular to the line of the singularity. See the geodesic chart here: math.stackexchange.com/questions/2929400 - It also shows that different particles end up in different "points" of the singularity ("points" in the asymptotic sense). $\endgroup$ – safesphere Nov 4 '19 at 15:29

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