Good I am glad that there are some good answers and considerations. I’ll reply in two sections because there appears to be two sub-threads.
As to the primary question of the smallest size that a black-hole can be and exist stably.
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Originally Posted by CraigD
For example, a 2e5 kg black hole has a lifetime of about 1 second, a 7e5 kg one about 1 year, and a 1e11 kg one about 1.4e10 s, about the current age of the universe according to Big Bang model. By way of comparison, 1e11 kg is just a bit more than the mass of a large artificial structure like the Three Gorges Dam.
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Okay, let me just clarify… you are talking about only the evaporating side of the equation… correct?
What about the other side of the dynamic? Consumption. Does a black-hole consume more when the density of compactable material is high? Deductively the answer must be, “Yes.” If a black-hole is in a pure vacuum then nothing could be consumed. As material is added to the surrounding matrix rates of consumption necessarily increase. Although there may be a maximum rate of consumption under a given set of conditions, altering such conditions, e.g., increasing pressure, could result in increased consumption rates. All this is important to the original question, because by increasing the rates of assimilation/accretion you could reach the dynamics necessary for stability at lower and lower masses.
This point loops back to your post when it is said
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Originally Posted by CraigD
In principle, a small black hole could be stable – that is, be at equilibrium, neither gaining nor losing mass – if the power of its infalling matter and radiation equals that of its Hawking radiation. For the cosmic background radiation – which all objects are more or less guaranteed to receive – a black hole of about 4e22 kg – about the mass of Earth’s moon has about this equilibrium.
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Perhaps I am misreading you, but it appears that you are saying that equilibrium for a black-hole only assimilating/accreting the energy from the CMB, but nothing else, will be stable at a mass of 4e22 kg. Am I reading you correctly? So, a smaller, yet still stable black-hole could be achieved under conditions where more energy/mass are being accreted. Is that correct?
To this line of inquiry, CraigD did appear to address these queries,
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Originally Posted by CraigD
(infalling matter couldn’t be used to stabilize an arbitrarily small black hole, because the exclusion principle limits the amount of fermionic mater that can occupy a given volume of space.)
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The problem is, following the link provided offers no evidence to support the notion that infalling energy would be interchangeable infalling mass to achieve black-hole stability. After all doesn’t the famous equation E=mc2 suggest an interchangeability between mass and energy? Nowhere on the link discussing the Pauli Exclusion Principle is it suggested that E=mc2 does not apply.
