Imagine a black hole that is fast-approaching its final exponential throws of Hawking evaporation.
Presumably, at all points in this end process there there will remain a region that identifiably remains "the black hole" until the the very end, as opposed to huge swarm of fundamental particles that is being radiated out from it.
As the mass of the black hole descends to that of individual particles, it would seem entirely feasible that the very last fermionic Hawking radiation event available to the almost-deceased black hole could leave it with an unbalanced charge, e.g. -1, and an unbalanced spin, say 1/2. It would also have some kind of mass of course, but that aspect of the final residue could be fine-tuned to any specific value by photon emissions of arbitrary frequencies.
After photon emission mass trimming, the resulting black hole residuum would reach a point where it is no longer be able to evaporate into any known particle, because there is no longer any lower-mass option available to it for removing the -1 charge and 1/2 spin. The black hole residuum will at that point be stuck, so to speak, stuck with exact charge, spin, and mass features of an electron.
And so my question: Is it an electron?
And if so, by equivalence, is every electrons in the universe really just a particular type of black hole that cannot evaporate any further due to the constraints of charge and spin conservation?
And if so, why are charge and spin so uniquely combined in such black hole remnants, so that e.g. a remnant of -1 charge and zero spin is not permitted, at least not commonly, and the mass is forced to a very specific associated level? Is there anything in the current understanding of general relativity that would explain such a curious set of restrictions on evaporation?
The full generalization of this idea would of course be that all forms of black hole evaporation are ultimately constrained in ways that correspond exactly to the Standard Model, with free fundamental particles like electrons being the only stable end states of the evaporation process. The proton would be a fascinating example of an evaporation that remains incomplete in a more profound way, with the three quarks remaining incapable of isolated existence within spacetime. The strong force, from that perspective, would in some odd sense have to be a curious unbalanced remnant of those same deeper constraints on the overall gravitational evaporation process.
This may all be tautological, too! That is, since Hawking radiation is guided by the particles possible, the constraints I just mentioned may be built-in and thus entirely trivial in nature.
However, something deeper in the way they work together would seem... plausible, at least? If an electron is an unbalanced black hole, then the particles given off would also be black holes, and the overall process would be not one of just particle emission, but of how black holes split at low masses. Splitting with constraints imposed by the structure of spacetime itself would be a rather different way of looking at black hole evaporation, I suspect.
(final note: This is just a passing thought that I've mulled over now and then through the years. Asking it was inspired by this intriguing mention of Wheeler's geon concept by Ben Crowell. I should add that I doubt very seriously that that my wild speculations above have anything to do with Wheeler's concept of geons, though.)
Answer
Yes and no.
Electrons - and all other elementary particles - may be viewed as microstates of very tiny black holes. As one considers increasingly heavy elementary particles (e.g. those in the Hagedorn spectrum of string theory), they increasingly morph into black hole microstates. When the elementary particle masses sufficiently surpass the Planck scale, most of the elementary particles look like typical black hole microstates.
So quantum gravity as we understand it today implies that there is a gradual transition from elementary particles and black holes.
However, if the elementary particles - very light black hole microstates - are (much) lighter than the Planck scale, the description of these "black holes" using the most naive equations of general relativity (Einstein's equations) becomes highly inaccurate. Corrections such as (powers of curvature tensors) $R^n$ to the equations of motion, and various quantization rules and other deformations from quantum mechanics, restore their importance – those can only be neglected in the very large size limit.
Consequently, most predictions made by classical GR are seriously inaccurate or downright wrong for the elementary particles if they are treated as black holes. For example, the charge/mass ration of an electron (or other known charged particles) vastly exceeds the upper limit defining "extremal" black holes in GR. Such black holes wouldn't be classically allowed, but this regime is highly non-classical, so these objects do exist with the known properties.
It is actually necessary for the charged elementary particles to behave as "not allowed" overcharged superextremal black holes. It's needed for regular large charged black holes to fully evaporate, which is needed for other reasons. All these claims are equivalent to the so-called weak gravity conjecture.
http://arxiv.org/abs/hep-th/0601001
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