Elementary particles are defined as particles having no internal structure - or at least none that we know. But we don't know, and maybe can never know, the internal structure of a black hole. So therefore as far as we're concerned they have no internal structure. Does that makes them (huge) elementary particles.
closed as off-topic by heather, user108787, Jon Custer, ACuriousMind♦, Norbert Schuch Sep 10 '16 at 12:53
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I think your premise is quite an interesting one, and one that I have a bit of a sweet spot for in my own heart. The basic idea, as you said, is that elementary particles share a property with singularities in that they have no internal structure. Most of the physics I know along these lines has come from the opposing perspective however, rather than "can we explain black holes with particle physics," it's been "can we explain particles as black holes."
If I am recalling my history correctly, some early papers from Einstein himself tried to construct classical physics as just the theory of spacetime with holes, vorticies, much like black holes. John Wheeler also did interesting work along these lines.
The fundamental idea (turning yours on it's head) that perhaps elementary particles are quite similar to black holes is not very new. Wheeler's attempt at fleshing out these ideas essentially ended up becoming absorbed under the umbrella of Geometrodynamics, and the quantum theory thereof.
No, not possible. They just don't come, nor are observed, with unique values of mass or spin, or any of the quantum numbers that are associated with elementary particles.
Elementary particles come in very specific quantum numbers, for spin, parity, and others. They also have, for each elementary particle type (e.g., electrons, down quark, Higgs boson, etc) their unique masses. And they are indistinguishable from another particle of their type.
ADDED EDIT (this paragraph) As @Holger Fiedler points out in his comment, that it's a little different for photons - my take on what he may mean is that since they have zero mass photons of different energies have different effects, though still in all cases they follow exactly the same laws, just their interactions are energy dependent. Of course, all particles interact differently at different energies, also following their same laws, but they can always be brought to rest (in some reference frame) and then any measurements on them give the identical results. Still, a 'small' difference for photons because of their zero mass. It does not seem to me to affect the argument of this answer.
Black Holes (BHs) come in a seemingly continuous values of mass, and spin. All the measured BHs have their mass determined, more or less, by how much mass-energy has gone into making them. There are BHs that have been observed and whose mass and in some cases spin has been determined (approximately), and there is no multiples of a given mass, there is no discreetness. Moreover, when they radiate gravitational waves they loose mass, usually in much smaller quantities than the masses of other BHs.
You might be able to argue that they are composed of many elementary particles, and be consistent with these observed features, but that does not help your case. Even if it were so, they would be composed of many elementary particles, sort of like a nucleus has a bunch of protons and neutrons, or a proton a number of quarks and a large number of gluons. But saying they are composed of many particles is quite different from what you are saying. Mainly since once any particle becomes part of a BH, we stop seeing any quality/property of that particle. Only the total mass and spin (and charge if they have any) is observable from a BH - due to the No Hair Theorem.
String Theory has a better hypothesis, that it is composed of strings, and using that they can reproduce the entropy of a BH. There is also the AdS/CFT conjecture that says it is the strings inside that are represented at the horizon by a Conformal Quantum Field Theory. But there's too many unknowns to know if any of that is true.