How little mass can a black hole contain and still be a "stable" black hole? What would the diameter be, in terms of the event horizon?
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2$\begingroup$ Online BH parameters calculator: xaonon.dyndns.org/hawking $\endgroup$– DarenWCommented Feb 25, 2013 at 22:15
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1 Answer
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In order to be "stable", the black hole's Hawking radiation temperature would need to be equal to the temperature of the cosmic microwave background, which is currently 2.7 K. (Assuming this is what you meant by "stable"?)
From Wikipedia:
"A black hole of $4.5 × 10^{22}$ kg (about the mass of the Moon) would be in equilibrium at 2.7 kelvin, absorbing as much radiation as it emits"
So then, the Schwarzschild radius of such a black hole would be:
$r_\mathrm{s} = \frac{2G(4.5 × 10^{22})}{c^2}$
= 0.00007m
Edit: Even if a black hole is slightly lighter than the above mass, it would still take an extremely long time to evaporate completely (on the order of $10^{40}$ years). And if the black hole is heavier than the above mass, it will still evaporate, but only after the CMB cools down sufficiently ($10^{100}$ years for supermassive black holes). With these kinds of time scales, the notion of "stability" starts to blur a bit!
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1$\begingroup$ Additionally: a large fraction, if not the majority, of physicists believe BHs of this size can exist. Nonetheless, that doesn't imply that they do exist. $\endgroup$ Commented Feb 25, 2013 at 22:36
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$\begingroup$ Which is comparable to the width of a human hair. $\endgroup$ Commented Feb 25, 2013 at 23:55
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$\begingroup$ @AlanSE what physicists would believe that such a BH 'couldn't' exist? $\endgroup$ Commented Feb 25, 2013 at 23:56
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$\begingroup$ @AlanSE Though most astrophysicists would be surprised if such things existed in nature - there aren't really any known mechanisms for producing such things. $\endgroup$– user10851Commented Feb 25, 2013 at 23:56
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$\begingroup$ @zhermes I recently stumbled on a very strange conversation, quora.com/Cosmology/Do-primordial-black-holes-really-exist and at first I thought it was being implied that these might not be possible, but on further reflection the statement "inflation rules them out" might have meant something other than what I had thought. $\endgroup$ Commented Feb 26, 2013 at 0:08