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Edit: Replaced black hole with neutron star, thanks to safesphere for his comment.

We're told that tiny volumes of matter have huge mass in a neutron star. For the sake of argument, if you had a 1cm cube of matter that weighed 1k tonnes and you bought it back to Earth, would the volume still be the same? If that's the case, why can't we create super dense matter in a lab? Or would it just be insanely hot?

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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/18981/2451 , physics.stackexchange.com/q/246061/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented May 16, 2018 at 13:02
  • $\begingroup$ Edit your question to change "black hole" to "neutron star". Then the question would make much more sense. $\endgroup$
    – safesphere
    Commented May 16, 2018 at 15:34
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    $\begingroup$ Possible duplicate of Why singularity in a black hole, and not just "very dense"? $\endgroup$
    – user4552
    Commented May 16, 2018 at 18:34
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    $\begingroup$ Hi Reece, Phys.SE usually only accepts changes to a question that leave the current answers on-topic. $\endgroup$
    – Qmechanic ♦
    Commented May 17, 2018 at 8:03
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    $\begingroup$ I second Qmechanic comment. If you want to ask about neutron stars instead of black holes, it's better to simply post a new question. But I can already tell you that, 'no', the volume wouldn't be the same here on Earth, unless you somehow kept it subject to the same huge pressures it's subjected to in the neutron star. $\endgroup$
    – stafusa
    Commented May 17, 2018 at 8:46

1 Answer 1

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A black hole exists as matter is compressed into a singularity. $F = {GMm\over r^2}$

This is because the gravity is so strong that everything is pulled together. Density being defined as the mass per unit volume(or otherwise, the degree of compactness of a substance). Adding mass to a black hole actually decreases its density. This is because a black hole doesn't increase the way a regular ball of matter does. The volume of a sphere is determined by the radius cubed, and so cubing the number two shows us that the volume is now eight times what it was before the mass was doubled. Density is mass divided by the volume. So if the mass of a black hole doubles, the volume grows eightfold what it was before. ${2\over8}=0.25$ So by doubling the mass, the average density of the black hole is decreased $0.25$ units.

I am digressing.

The point is that at a singularity, things are "infinitely" dense regardless of what they weighed before.

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  • $\begingroup$ The first paragraph doesn't make much sense, because there is no logic linking the first sentence with the equation. And the Newtonian force law doesn't apply here, either. The second sentence seems to refer to the mass of the black hole divided by the volume inside the event horizon, which also doesn't make much sense, both because the geometry isn't that of a sphere and because what's inside the event horizon is a vacuum. $\endgroup$
    – user4552
    Commented May 16, 2018 at 18:37
  • $\begingroup$ @BenCrowell Let me honest with you. I don't even answer questions on this app. The above answer was courtesy of a classmate who was using my phone for research purposes. $\endgroup$
    – Aleksey Antonovich
    Commented May 16, 2018 at 19:27
  • $\begingroup$ "research purposes"..? just curious $\endgroup$
    – William Martens
    Commented Nov 15, 2022 at 15:52

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