From: intuitionist1@gmail.com   
      
   > [[Mod. note -- Two points:   
   > * There's good reason to think that actual black holes in the universe   
   >   do not have r<0 regions.  That is, r<0 regions are only present if   
   >   you have *vacuum* Schwarzschild/Kerr solutions, with no matter anywhere   
   >   in the universe, and in particular, no matter ever present near to   
   >   or inside the black holes.  If you form black holes by collapsing   
   >   matter any time after the big bang, I don't think you get r<0 regions.   
   > * If you form multiple-black-hole spacetimes by collapsing matter any   
   >   time after the big bang, so far as we know you don't get multi-sheeted   
   >   Einstein-Rosen spacetimes, either.   
   > -- jt]]   
      
   It seems that you have in mind specifically astrophysical black hole   
   candidates, which are clearly extremely complex objects.   
      
   If we restrict ourselves instead to tiny (i.e. sub-elementary-particle)   
   scales, and assume that _only_ particles of class A and B initially exist,   
   and that they have very tiny masses, and also that they collapse to form   
   very tiny naked ring singularities (i.e leading to the fast Kerr solution   
   specifically), then that would be a more useful scenario to consider.   
      
   The ring singularity would then bound a disc connecting the two regions,   
   and there would be no problem with particles crossing the disc from one   
   sheet to the other in that case (such trajectories are known to exist and   
   they do not cause the wormhole to pinch shut before the particles can   
   cross). Applying the argument I made earlier there would have to be   
   particles of all four types present in each region even before the   
   singularity forms.   
      
   It is not even necessary to have multiple black holes or multiple ring   
   singularities. As soon as a single ring singularity forms, particles of   
   class A and B will cross from r>0 to r<0 and so in r<0 there will be   
   particles present of all four classes, and once again we would need to   
   extend GR to a bimetric theory on a double-sheeted spacetime.   
      
   To avoid this conclusion you could try to discard  the r<0 region, but   
   this is a mathematically valid part of the solution which can be reached   
   by the particles present, so I see no justification for doing so.   
      
   If you have a reference to a (classical) proof that r<0 regions cannot   
   physically form in any of the Kerr-type solutions, I would appreciate it if   
   you could mention them here.   
      
   [[Mod. note --   
   I don't know of any way to *form* a sub-elementary-particle--sized   
   black hole (if it wasn't already present in the big bang).  That is,   
   I don't know of any formation scenario for collapsing that small an   
   amount of mass-energy to form a black hole.  And if you did collapse   
   it, I don't see any reason why it would form a naked ring singularity,   
   i.e., why you'd have |J|/M^2 > 1.  (If you had that much angular   
   momentum, wouldn't the "centrifugal barrier" prevent collapse?)   
      
   In general, if you do form a black hole by collapsing "stuff"   
   (mass-energy), I don't think you get an r<0 region.  Rather, the   
   "stuff" replaces the r<0 region (see, e.g., the diagram in MTW box   
   33.2 section G.1, with the text there stating that the r<0 region   
   "gets fully replaced by the interior of the star that collapsed to   
   form the black hole" (this statement doesn't depend on the size of   
   the "star" in question, at least so long as we're dealing with the   
   classical Einstein equations).   
      
   If you did have such a ring singularity (maybe already present in   
   the Big Bang?), would it be stable?  All the Einstein-Rosen bridges   
   I've seen are highly unstable if the black holes accrete any   
   mass-energy.   
      
   Of course, if we're going to talk about black holes with   
   "sub-elementary-particle" sizes, quantum gravity effects are surely   
   important, so arguments based on the classical Einstein equations   
   are rather dubious.   
   -- jt]]   
      
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