# Are electrons just incompletely evaporated black holes?

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.)

• I think here is the mismatch : " 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." It will stop being a black hole long before its mass reaches the electron mass. centaurihome.net/swartz.php . The degenerating black hole will no longer be able to trap light and define an event horizon. It will be a neutron star or some such. – anna v Sep 1 '13 at 19:08
• Have I ever mentioned that many of your question titles make me cringe and reach for the close button thinking that they signal yet another kook? I swear you do this to me more often than not. – dmckee Sep 2 '13 at 3:41
• you might be interested in this paper : cds.cern.ch/record/1314757/files/plb.697.434.pdf . tiny black holes still carry a lot of energy in their decay/evaporation – anna v Sep 2 '13 at 19:17
• Thanks all for your comments - I think enjoyed dmckee's the most! To clarify: In my day job we try to dissect sentience well enough to replicate it. Few things are more mysterious in the pursuit of sentience than the way human intelligence sometimes... jumps... from some known view to some very different one. In a disciplined sentience, quality checks then rapidly eliminate 99% or more of such jumps. But without a willingness to entertain such leaps, sentience quickly devolves into "fast but dumb" rote behaviors. It is a lack of checks that leads to true kookery, not the lack of exploration. – Terry Bollinger Sep 3 '13 at 5:17
• @BenCrowell I found this answer which supports your statement that a black hole remains a black hole,until at the end there is an explosion because "it’s radiating away energy faster and faster" thenakedscientists.com/HTML/questions/question/3183 – anna v Sep 4 '13 at 18:08

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

Classically, a spinning, charged black hole has constraints on its angular momentum and its charge in relation to its mass. Otherwise, there is no event horizon, and we have a naked singularity rather than a black hole. An electron violates both of these limits, so electrons definitely can't be black holes.

We could ask whether electrons are instead naked singularities. However, we don't observe that electrons have the properties predicted for these naked singularities. For example, the naked singularities would have closed timelike curves in the spacetime surrounding them, which would violate causality, but there is no evidence that electrons cause causality violation.

A separate issue is that in a scenario where these were originally black holes (presumably primordial ones), then I also don't think it's possible for them to evolve into naked singularities. This would violate what seems to be pretty solid support for cosmic censorship. But I suppose you could just postulate instead that there were primordial naked singularities.

• Ben Crowell, nice points, thanks. But I think I must be missing something here: Where does the "oddness" of a black hole (or singularity) end up in an evaporation event? Is that even really known? I gather that Polchinski et al have recently raised some interesting points regarding the conflicts between several seemingly reasonable assumptions about hole annihilation. I like anna v's tact - that is, that the hole falls apart before reaching single-particle scale - but even that seems unsatisfying in terms of where the "oddness" ends up. – Terry Bollinger Sep 3 '13 at 5:42
• @TerryBollinger: Are you just using "oddness" as a synonym for "singularity?" The singularity goes away when the evaporation of the black hole is complete, or at least that's the current conventional wisdom. The Polchinski paper looks like it's about firewalls -- how would that be relevant here? I don't think anna v's depiction is correct. A black hole certainly doesn't evolve into a neutron star as she suggested. – Ben Crowell Sep 3 '13 at 15:28
• Ben, when you said "For example, the naked singularities would have closed timelike curves in the spacetime surrounding them... but there is no evidence that electrons cause causality violation"... it made me curious quantum forms of time loops. The QED integral of all possible histories for an electron includes a form of causality violation, since for example it can contain time loops. Are the math models for GR singularity-induced time loops and QED integrals of possible histories similar enough that they could be represented as part of a single framework? A sort of "singularities integral"? – Terry Bollinger Sep 30 '13 at 1:19
• @TerryBollinger: My field theory isn't that strong, so I'm probably not the best person to ask. – Ben Crowell Sep 30 '13 at 2:02
• Ben, thanks, it's just an intriguing and unexpected similarity between QED and GR that never occurred to me until you made that comment. Any good mutual experts on those two fields out there in stack exchange? I have to admit, though very far-fetched, the idea that quantum uncertainty could in any way be related to singularity time-loops fuzzing out local reality is delightfully amusing... :) Maybe I'll risk an actual question, and probably deservedly get fried good for it... :( – Terry Bollinger Sep 30 '13 at 3:11

A black hole cannot evolve into an electron. To properly describe an electron, you need two spinors coupled for the Dirac Electron, where the coupling constant is the mass of the electron.

That being said, a black hole and a neutron can both be described as uncoupled spinors.

• Welcome to physics.SE! A black hole can (given what we think we know about Hawking radiation) evolve into essentially any combination of particles, subject only to conservation of total mass-energy, charge, and angular momentum. All other conservation laws of physics (e.g., conservation of lepton number) are believed to be violated in black hole evaporation. There is a nice discussion of this in Wald on p. 413. Although Hawking radiation is typically spoken of casually as being purely made of photons, it actually contains all possible types of particles. – Ben Crowell Sep 2 '13 at 18:37

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