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How big can a black hole become and how small can a black hole become?(minimum and maximum dimensions of a black hole)

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up vote 9 down vote accepted

Primoridial black holes can be found (hypothetically; there is no experimental evidence yet) of any small size above the Planck mass. Stellar black holes, however, cannot have a mass below the TOV limit (1.5 to 3 solar masses)

There does seem to be an upper limit1 of 50 billion solar masses. However, I suspect2 that this takes into consideration formative constraints (i.e. the constraints posed on the formation of such a BH); and does not prohibit such a black hole from existing. After all, the Schwarzschild metric certainly does not impose limits on the size of a black hole.

Note that talking about the limiting dimensions of a black hole is slightly meaningless as the dimensions change in different reference frames. It is far easier to talk about the mass of a black hole; the radius can be calculated in various frames from that information.

1. Natarajan, P. and Treister, E. (2009), Is there an upper limit to black hole masses?. Monthly Notices of the Royal Astronomical Society, 393: 838–845. doi: 10.1111/j.1365-2966.2008.13864.x

2. but cannot confirm yet; I will have to read the paper more thoroughly

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Primordial black holes "can be found"? That's a confusing way to word that statement, since it suggests that they exist. And that there's no evidence for. –  Stan Liou Dec 21 '13 at 8:54
    
@stan fixed, thanks. Though iirc there's a lot of theoretical evidence showing that our universe should have them. –  Manishearth Dec 21 '13 at 16:56
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theoretically there should be no maximum size/mass of a black hole, or you could say the maximum mass would be if it contained all the mass in the universe;

although the minimum dimension of a black hole would be a Planck length, the minimum mass of a stable black hole is 3 solar masses;

a black hole that has a mass less than 3 solar masses will evaporate, transforming itself into radiation (energy); the smaller it is, the faster it evaporates; if it is small enough, it will instantly turn into a flash of hard radiation;

http://en.wikipedia.org/wiki/Hawking_radiation

if you know the mass of a black hole you can calculate its radius and if you know its radius you can calculate its mass; note that a curious thing about this equation is that it shows a stellar mass black hole having a high density, whereas a supermassive black hole having a density that decreases as the black hole increases in mass;

http://en.wikipedia.org/wiki/Schwarzschild_radius

so you could transform anything you want, such as your pencil, into a black hole if you wanted to, and could compress it into the required size for it to become a black hole; it is just that it would immediately transform itself (evaporate) completely into a flash of hard radiation, because a pencil is less than the stable black hole mass (3 solar masses);

this is why the CERN experiment could never have created a black hole to swallow the Earth - a subatomic black hole, even one with the mass of the entire Earth, or the Sun, would evaporate before swallowing anything; there is not enough mass in our solar system to make a stable (3 solar mass) black hole;

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The first part is outright wrong. All (non-extremal) black holes radiate, and there's absolutely nothing qualitatively special about three solar masses in that regard. –  Stan Liou Dec 21 '13 at 8:57
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