# How is it possible to compress matter infinitely like in a black hole?

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.

• You left out a lot of zeros! – G. Smith Oct 28 '19 at 2:20
• According to the Schwarzschild metric, the volume inside the black hole is infinite, so the average density is zero. – safesphere Oct 28 '19 at 7:18
• @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? – The_Sympathizer Nov 4 '19 at 8:41
• @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. – safesphere Nov 4 '19 at 15:49

• "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. – safesphere Nov 4 '19 at 8:29