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Okay, picture a planet so massive, a black hole has formed in its center. The minimum mass of a black hole is 22 micrograms, or the Planck mass, and whatever the core is made of, it needs to be compressed until there’s a point where the escape velocity is at least the speed of light. If we go with a terrestrial planet like Earth, how massive would the planet need to be for a black hole to form at its core from the sheer pressure?

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    $\begingroup$ I might be wrong about this, but aren't black holes usually formed from stars? In other words, the mass of the planet would need to be the mass of a star, which would make it a star? Also, I'm pretty sure you can't get a black hole in the middle of a planet without the planet becoming part of the black hole. Black holes are the essence of a vacuum, which means the planet would collapse. $\endgroup$ – JBH Dec 6 '20 at 22:43
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    $\begingroup$ That's not how gravity works. If it's massive enough to create a black hole (for any reason and in any way), the entire planet will collapse into a black hole. The core is not actually separated from the mantle or the crust. If, magically, the BH formed without initially collapsing the mantle, the mantle would collapse IMO in hours to days. You seem to have no idea what forces are in play here. I'd need a hard-science proof that a black hole could exist in any way within a structurally sound planet. $\endgroup$ – JBH Dec 6 '20 at 23:18
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    $\begingroup$ What about having the Black Hole first and then the planet? E.g. have a "Dyson Sphere" like object around it? $\endgroup$ – Imago Dec 7 '20 at 7:38
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    $\begingroup$ I think you want a microscopic pre-existing (perhaps primordial) small black hole in the center. It could be arbitraily small, close to evaporating. Such a small black hole would perhaps not lead to the quick destruction of the planet. $\endgroup$ – Peter - Reinstate Monica Dec 7 '20 at 10:08
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    $\begingroup$ Note: For something vaguely similar, it would be within the known laws of physics for a highly advanced civilization to build a rigid artificial structure around a black hole using "active support": your most important girders are Great Circles, and they are really tubes with mass inside moving faster than orbital speed to provide the force to counteract gravity. $\endgroup$ – Charles Staats Dec 7 '20 at 13:33
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Your planet needs to be about 722500 times more massive than Earth for its core to undergo collapse into a black hole.

Leaving aside the small detail that at this point your "planet" would look and behave like a star larger than the Sun, because it would be a star larger than the Sun, what will happen shortly afterward is that the rest of it will disappear in the black hole as well, making it bigger. I can't say how long exactly that would take, but the "it's a thing with a black hole at the center" would likely last no more than a couple of seconds, after which there would be just simply a black hole with the mass of thing that was there before it.

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    $\begingroup$ No, it will not take millions of years. Typical stars collapse within seconds, I did not exaggerate that bit. $\endgroup$ – Darth Biomech Dec 7 '20 at 0:12
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    $\begingroup$ It's a matter of pressure. Typical stars do live for millions of years before collapsing into a black hole, though the collapse does take just a short moment to complete when it comes. But an artificial star as proposed in the question? It could not generate enough energy to compensate for gravity at all (iron is stellar ash in terms of fuel), so it would become a black hole faster than a regular star. Darth Biomech is really not exaggerating. $\endgroup$ – The Square-Cube Law Dec 7 '20 at 0:33
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    $\begingroup$ To add to that, the main reason that prevents young stars from collapsing is the radiation pressure from within the star's core. There are literally too many photons being generated that they keep stuff from compressing more. That's why stars live millions of years before collapsing (and why old red giants are so big, I suppose) - collapse happens as soon as there are not enough photons being created by the fusion process to counteract the gravity compression. $\endgroup$ – Darth Biomech Dec 7 '20 at 0:38
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    $\begingroup$ @TysonDennis Pressure requires something to push against. The black hole provides nothing to push against, the matter simply goes down--the only resistance will be from the compression of the infalling matter. $\endgroup$ – Loren Pechtel Dec 7 '20 at 0:52
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    $\begingroup$ You could put a black hole at the center of a Dyson sphere. It's just not gonna form naturally. And the solar panels are just going to collect dust. $\endgroup$ – candied_orange Dec 8 '20 at 4:05
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No

A natural occurring black hole that comes into existence due to mass collapsing onto itself must have more mass than the Tolman–Oppenheimer–Volkoff limit, which has been estimated to be around 2.17 solar masses.

There are no planets that are more massive than stars. At around 13 times the mass of Jupiter (in other words, at around 4,134 times the mass of Earth) a planet would be fusing stuff at its core to become a brown dwarf. That would still be way less than a solar mass, but that would also no longer be a planet.

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    $\begingroup$ @TysonDennis it does require require handwaving - I am going for realism due to the astrophysics tag. Please see this other question in the site: Is there a theoretical maximum size for rocky planets? $\endgroup$ – The Square-Cube Law Dec 6 '20 at 23:08
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    $\begingroup$ @TysonDennis I'd steer clear of handwaving it as a natural occurrence, since it simply will not occur naturally. You might be able to get away with handwaving via a hyper-advanced civilization, since you can pretty much chalk it up to physics and technology we don't yet understand. $\endgroup$ – WillRoss1 Dec 7 '20 at 0:51
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    $\begingroup$ @TysonDennis ... and a hyper advanced civilization would not want to endanger the existence of their planet by placing the single most dangerous thing in the universe at its core! $\endgroup$ – cmaster - reinstate monica Dec 7 '20 at 11:08
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    $\begingroup$ @nwp yes, that's what I meant. $\endgroup$ – The Square-Cube Law Dec 7 '20 at 13:18
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    $\begingroup$ I'm not sure if it makes much practical difference here, but it's probably worth noting that the TOV limit is an (idealized!) upper limit to the mass of a neutron star, rather than the lower limit to the mass of a black hole. There's also considerable scatter in known values, particularly given certain observations of NS systems. Maybe the difference isn't relevant here, but I think it would be better to be precise. $\endgroup$ – HDE 226868 Dec 7 '20 at 15:19

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