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Imagine a box with two characteristics:

  1. It is indestructible, it can't be deformed or torn apart.
  2. It can shrink to any precise size regardless of the opposite forces.

Let's assume the box starts with a size of 10 m³ and contains gas molecules. As you shrink the box, molecules increasingly push against the walls of the box. At some point, the matter in the box is so compressed that it becomes a black hole.

I'm thinking that since the matter went from trying to expand to generating its own gravity toward a compact point, there must be a point where the matter was neither trying to expand nor was it a black hole, so it was in a neutral state.

Is this assumption wrong? If so, what does the matter go through before being a black hole? Is there even a point where an object goes from not being a black hole to being a black hole?

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  • $\begingroup$ 1) an un-deformable box violates special relativity. See: Born Rigidity. $\endgroup$
    – JEB
    Commented Sep 13, 2021 at 20:29
  • $\begingroup$ You have to put a lot of gas into your box. A black hole with the radius of a proton (0.85 fm) has a mass ~572 million tonnes. See vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator $\endgroup$
    – PM 2Ring
    Commented Sep 13, 2021 at 20:30
  • $\begingroup$ Can't any object become a black hole if compressed enough ? $\endgroup$ Commented Sep 13, 2021 at 20:37
  • $\begingroup$ @SamuelFyckes "Can't any object become a black hole if compressed enough ?" - A black hole is a concept in General Relaticity, which is a classical theory inapplicable at subatomic sizes. $\endgroup$
    – safesphere
    Commented Sep 14, 2021 at 2:02
  • $\begingroup$ @safesphere Fair point. Relativity doesn't "know" what matter is made of. OTOH, we don't know at what scale quantum gravity effects become significant, but it's probably within a few orders of magnitude of the Planck length, i.e., much smaller than a proton. $\endgroup$
    – PM 2Ring
    Commented Sep 14, 2021 at 5:04

2 Answers 2

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Astronomical objects made of gas/plasma in which outward pressure forces are in balance with inward gravitational attraction are called stars.

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    $\begingroup$ I imagine that the balance would be a little fragile, isn't it ? And you're telling me that at some point my object would be an extremely small star ? What happens in the process, what are the steps ? $\endgroup$ Commented Sep 13, 2021 at 20:36
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    $\begingroup$ @SamuelFyckes Fortunately the balance is actually very stable. Stars come in a wide range of sizes and temperatures and have typical lifetimes of billions of years. See en.wikipedia.org/wiki/Stellar_evolution for details. $\endgroup$
    – gandalf61
    Commented Sep 13, 2021 at 20:43
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    $\begingroup$ @SamuelFyckes I see what you mean. For example, if we forcefully compress the Earth to the size of a peanut, what would be the equilibrium point? There wouldn't be a stable one. You'd have to pass the density of the neutron matter, so it'll be a runaway process in one direction or another. $\endgroup$
    – safesphere
    Commented Sep 14, 2021 at 2:20
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In your example the forces in question that have to be in balance are the rigidity of the box walls and the ever increasing pressure of the gas (assuming a totally ideal gas that would never condense). The reason a black hole eventually forms is that matter is in so small a space that the local geometry warps enough so that "outward" is no longer an available direction.

In a star, rather than a rigid box you have the weight of all the matter above it compressing the core, so much that eventually no molecular or atomic or subatomic interactions can keep the matter far apart enough to prevent this same distortion of space time

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  • $\begingroup$ "the forces in question that have to be in balance are the rigidity of the box walls and the ever increasing pressure of the gas" - This is not what the question is. The OP is asking about a balance in the state of matter when the box no longer puts any pressure on the matter inside. $\endgroup$
    – safesphere
    Commented Sep 14, 2021 at 7:24

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