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It's the spherical aspect of these celestials bodies that makes me think about this.

Could planet Earth have started itself with a tiny black hole?

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One of my favorite fun facts about physics is that small black holes could indeed exist inside of the sun — or even any planet or moon. In fact, none other than Stephen Hawking himself actually suggested that this was a possible resolution of the "solar neutrino problem" (which has since been resolved with another explanation), "pulsarquakes" (now called "glitches"), and even Weber's claims of gravitational-wave detections (which have been discredited). You can read the paper in which he suggested this for yourself here. Although these claims are not currently accepted, the point is that Hawking (correctly, as far as we currently know) suggested that the sun could contain a black hole of as much as $10^{17}\mathrm{g}$, which would only have a radius of about $10^{-11}\mathrm{cm}$. This is so small that even inside the sun, particles couldn't fall into it at a very high rate, which means that the sun could actually survive for about as long as it has survived with little significant effect. On the other hand, there may be far smaller black holes, with even less effect, so it's quite possible that the earth itself contains one or more black holes.

Now, as for the question of whether or not such black holes could form the seeds that lead to the gravitational collapse of dust into planets — that's not really likely. They must be small enough to not consume the planet over very long time scales, which means that they don't really have very significant masses. On the other hand, the range of energies of particles that could be captured by such black holes is quite small, especially compared to typical energies involved in gravitational collapse of dust and gas into a planet. But even then, most of the particles that are "captured" wouldn't go into orbit around the black hole or anything like that; they'd just get sucked in. So no planet would form, it would just be a growing black hole. And it would grow so slowly that it would never get very big — remember that even inside the sun, a black hole wouldn't grow that quickly. Moreover, planets are roughly spherical (in fact, by definition of a planet) because they are massive enough that their own gravity can overcome stresses that would stop the planet from being spherical. The reason this happens, in turn, is because gravity is fundamentally a spherically symmetric force — it is linear, so you just add the contributions from different parts of a source; and it depends only on distance from each part of the source, rather than direction to that part of the source.

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  • $\begingroup$ The Hawking paper is almost 50 years old, and it contains a lot of material that is extremely out of date. For example, it refers to supposed detections of gravitational waves by Weber, which have since been discredited. Today we have much more information on primordial black holes: en.wikipedia.org/wiki/Primordial_black_hole $\endgroup$ – Ben Crowell Sep 16 '18 at 1:17
  • $\begingroup$ @BenCrowell Yes, the main point of the paper was his discussion about primordial black holes — and in typical Hawking fashion he suggested that they could explain "pulsarquakes", Weber's "detections", and the solar neutrino problem as I mentioned. (I just find that to be the most interesting of Hawking's suggestions.) But the point relevant to this question and my answer is that it's really not a crackpot idea to suggest that very small black holes could exist inside of long-lived objects — which is a point from his paper that stands to this day. $\endgroup$ – Mike Sep 16 '18 at 16:54
  • $\begingroup$ In discussing whether idea X is a crackpot idea, it matters whether you discuss X in the context of 1971 or the context of 2018. Phlogiston and spontaneous generation were not crackpot ideas in the 19th century, but they are crackpot ideas now. $\endgroup$ – Ben Crowell Sep 16 '18 at 17:11
  • $\begingroup$ @BenCrowell Valid points, but not relevant here. None of the three ideas Hawking raised were then or are now considered crackpot ideas; two of them turned out to be incorrect, and the third is not thought to be the answer to a still-unsolved problem. Even Weber isn’t seen as a crackpot; I’ve personally discussed him with Kip Thorne several times, and only heard positive things—wrong though he was. In any case, those are all tangential points that Hawking brought up unrelated to my point which is that it is possible that very small black holes could exist inside larger bodies. $\endgroup$ – Mike Sep 16 '18 at 23:59

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