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For something to be a blackhole, it must have gravity and the radius must be smaller than the schwarzschild radius for its mass.

-Electrons have gravity

-Electron are theoretically believed to be infinitely small points

Since it has gravity it is capable of being a black hole. Since its radius is infinitely small, it must have a schwarzschild radius and thus be a black hole.

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There is no universally accepted quantum theory of gravity.

Quantumly, the "shape" of a fundamental particle is a very fuzzy notion - we know that states are often not localized, so it is wholly unclear what it means to say "the electron is pointlike". The proper formal interpretation of a "pointlike particle" is simply a particle that is not composite - has no substructure we know of.

But the electron is not believed to be a "miniature black hole" because no one expects gravity to work exactly as in GR at the quantum level. Your question is meaningless at the current state of knowledge because black holes are classical macroscopic objects, and the "pointlike structure" of the electron is not meant in the sense that it is a classical point particle.

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    $\begingroup$ It should be said that unless the Schwarzschild radius is bigger than about the Compton wavelength, it has no real meaning. $\endgroup$ – Ryan Unger Feb 19 '15 at 1:09
  • $\begingroup$ The smallest size of the black hole is 10^22 times the size of the electron, by weight. And this is a quantum scale. $\endgroup$ – wendy.krieger Feb 19 '15 at 12:06
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Electrons are very close to the energy of self-capacitance of a quantum of charge.

The size of the electron is very close to $r_e$, the energy supposed if one tries to charge a sphere of that radius with a single electronic charge, ie $mc^2 = e^2/4\pi\epsilon r_e$.

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  • $\begingroup$ What "size" are you referring to? The OP states they are points, as noted on Wikipedia with a citation of a textbook. Experiments indicate it is smaller than 10^−22m in radius. $\endgroup$ – JDługosz Feb 19 '15 at 10:09
  • $\begingroup$ OP suggests points because electrons are 1/18000 times the size of the atom. The size of the electron varies according to the experiment, but the presence of a linear scale at any particular size is not definitive. A quick google search on 'electron size' tells us they can't even get the shape consistant. OP cites no reference or formula, nor was i to find this number. $\endgroup$ – wendy.krieger Feb 19 '15 at 12:05
  • $\begingroup$ So what size is close to r sub e ? $\endgroup$ – JDługosz Feb 19 '15 at 12:10
  • $\begingroup$ It's the classical electrical radius, around 2.86 fm. $\endgroup$ – wendy.krieger Feb 19 '15 at 12:12
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Well, according to the wild ER=EPR conjecture by Maldecena and Susskind, two entangled electrons are connected by a quantum wormhole. The mechanism and details of this quantum wormhole are left unspecified by these authors, though.

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