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According to quantum mechanics electrons don't behave like everyday objects. Would this prevent the formation of a black hole? If so why?

Also, assuming they behave like everyday objects, at what size would they become a black hole?

I ask because according to various sources an electron could be a point, have a 'classical electron radius' of $10^{-15}$ m, or a diameter of planck's length ($10^{-35}$), and it seems to me that even though an electron has very little mass having no size would make it immeasurably dense.

Edit: Here's a wikipedia page I found that directly answers this question (Black hole electron - http://en.wikipedia.org/wiki/Black_hole_electron).

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  • $\begingroup$ In quantum mechanics an electron is treated as a point particle; e.g., its density operator is a delta function (infinite at one location, zero elsewhere... basically... to be more exact it is a delta functional, but whatever). If you are looking for a good quantum theory of gravity, you have your work cut out for you. Good luck getting funding. $\endgroup$ – hft Sep 3 '15 at 5:12
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The rest mass of an electron is estimated to be about 9.1 * 10^-31 Kg. The Schwarzschild radius defines the maximum size sphere which any mass may occupy in order to be a black hole. The Schwarzschild radius for an object with the rest mass of an electron would be about 1.4 * 10^-58 meters.

But the Planck length is about 1.6 * 10^-35 meters. Quantum gravity becomes important in understanding what happens at this scale. As there currently is not a generally accepted theory of quantum gravity, and as the Schwarzschild radius for an electron is significantly smaller than the Planck length, it's uncertain that General Relativity, which predicts and describes black holes, would apply. So I don't think that one can predict an object with the mass of an electron would ever become a black hole.

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  • $\begingroup$ Thanks for the link to the Schwarzschild radius calculator. That was exactly what I was looking for. $\endgroup$ – Paul Sep 3 '15 at 13:23

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