# How complete is our understanding of general-relativistic solutions for extremal black holes?

Putting aside quantum mechanics (or at least putting aside the question of fermions), is our knowledge of extremal General-Relativity solutions good enough that we would be able to rule out a classical theory of spinning charged relativistic particles based on extremal black holes? I ask this in the context of my curiosity about geons and in the spirit of recognizing the difficulty of quantizing a system whose classical theory is not well understood.

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Spinning black holes are not geons. Geons are gravitational bound states of light/gravitons. – Ron Maimon Jan 15 '12 at 3:50
Ops I guess I was using the term overly generally; I'll remove the parenthetical, thanks. – user1247 Jan 15 '12 at 3:56
You should also know that within string theory, all matter is an excitation of an extremal black hole of one kind or another. The duality between string matter and classical black holes is of a nature that the two differ only in size. If you dualize fundmental strings so they become heavy, and T-dualize them to become extended, and stack them up on top of each other so that they have a macroscopic mass and charge, they smoothly become classical black holes. The identity is exact enough that all properties of black holes are translatable to string theory, through AdS/CFT. – Ron Maimon Jan 15 '12 at 3:59
@Ron Maimon: "The duality between string matter and classical black holes is of a nature that the two differ only in size" -- this gets at my unanswered comment in the "Could strings be geons" thread. Is the duality such that plank-scale string matter is dual to a cosmic-scale black hole, or is the duality between objects of roughly the same size? I want to know if it makes sense to think of fundamental particles as tiny extremal black holes. The existence of a duality with black holes doesn't alone answer that; the duality needs to be between experimentally similar objects. – user1247 Jan 16 '12 at 23:01
The "duality" means that the mathematics of classical black holes emerges from large stacks of strings and branes. This is the mathematics. In terms of physics, the fundamental particles in string theory are all tiny black holes, of quantum size. The only reason people say "duality" is because the classical mathematics of black holes does not apply to such tiny ones as describe elementary particles, the emergence of the classical Einstein solution come from stacking a lot of string stuff on top, to take the classical limit. This has been understood since the 1990s. – Ron Maimon Jan 17 '12 at 2:33