Quote: "One has reasons to suspect that this matter is emitted from the black hole nonthermally, more or less as it came in, after doing a traversal of the interior regions." Ron Maimon in Do black holes accelerate in spin as they obtain more mass?

What are these reasons and how can this matter escape a black hole ?


The reason is that the classical solution allows matter to escape. If you consider a near-extremal Reissner Nordstrom black hole:

$$ ds^2 = - f(r) dt^2 + f(r) dr^2 + r^2 d\Omega^2 $$ $$ f(r) = 1 - {2M\over r} + {Q^2\over r^2} $$

where extremality means Q=M so that

$$ f(r) = ( 1 - {Q\over r})^2 $$

You find that there are two horizons, which are the two zeros of f(r) for $r>0$. The zero at greater value of r is the event horizon, since it is a boundary for r and r is spacelike, the one at smaller value of r is the Cauchy horizon, since it is inside the black hole where r is timelike.

Classically, the motion of a particle falling in is to cross the event horizon, cross the Cauchy horizon, turn around before r=0, come out the Cauchy horizon going the other way in r, and come out the event horizon going the other way in r. This entire back-and-forth is required classically once you cross the horizon.

The problem is that each region is linked to the previous region by a process of extension, so that if you take the classical picture seriously, you get that the region that the particle escapes to is a different region than the region that the particle entered from. This is the "wormhole to another universe" interpretation of Reissner Nordstrom black holes which was suggested by Carter in the 1960s.

The problem with this interpretation, going to another universe, is that it is clearly incompatible with unitarity. It is also incompatible with the following simple fact--- the radius of the event horizon is the same in all the universes (this follows from the fact that they are extensions of the same solution, so the r-form of the metric is identical in all of them). If you have a particle enter in one branch, the event horizon grows. If it leaves in another branch, the event horizon shrinks. This means that the two horizons are mismatched.

Puzzled by these types of paradoxes, Penrose decided that the Cauchy horizon must be a dead-end, despite the fact that the classical solution does not show it. He proposed that there is an instability that makes the Cauchy horizon singular, so that nothing can cross this boundary. One reason to suspect this is that as you cross the Cauchy horizon, you classically can recieve highly blueshifted signals from the entire future of the black hole, and this seems like it will make a wall of ultraviolet energy which kills you.

But simulations and analysis of the singularity at the Cauchy horizon didn't show a non-traversible singularity, rather a milder step-jump in the metric, like a hard-wall of matter. This kind of thing will burn you, but it won't stop you from going through. Further, the instability is dependent on perturbations, and without external perturbations, you don't get the hard wall, so the size of the wall is miniscule if the black hole is left alone forever.

So there is no real evidence for Penrose's picture. It's just a guess. I don't believe it, because this is not what happens in AdS/CFT models.

To see what happens there, consider a SUSY gauge theory which describes N stacked branes. Pull one brane out, and give it a little velocity toward the others. This brane then moves slowly to join with the others, and then becomes noncommutative at the point of joining. The standard lore, due to Gubser, is that it then thermalizes because of the noncommutative degrees of freedom. But the argument I find unpersuasive. I don't understand how something at zero temperature can thermalize so effectively. I think it just bounces out again after a certain time.

The interpretation of this is that there are stable oscillations possible next to an extremal black hole, in and out. This is born out by looking at the r as a function of proper time on a geodesic--- it makes a harmonic oscillation near the horizon for extremal Reissner Nordstrom. This oscillation is understandable as the motion in the near-horizon AdS metric, and if you have a bunch of bound objects, they oscillate together, and their relative positions are just describing AdS motion.

This is the AdS/CFT limit in which the extremal black hole (at least in higher dimensional analogs) becomes a gauge theory on the boundary of AdS. The objects in this theory are doing oscillations in and out in r, and they are crossing the two horizons again and again, except in their own proper time.

The only way I can see to reconcile these pictures is if the classical solution is glued, so that coming out in "another universe" is coming out in this universe. This requires that you identify all the continued exterior solutions with the exterior solution in this universe. I don't know the gluing, but I am pretty sure it must exist, since this is the only way to resolve the paradoxes that I can see (that, or the magic Cauchy singularity that I don't believe exists and nobody has a persuasive argument for, other than resolving these paradoxes).

There is no real clue for this gluing from classical gravity, other than you don't want to come out before you came in. Any such gluing requires strange effects:

  • When matter is coming out, it can come out in either direction in t, since t is a spatial variable. This requires the gluing to do some nontrivial time-reversing operation to be consistent, perhaps ejecting the matter as reflected antimatter.
  • The gluing always introduces classical closed timelike loops, but these are sort of ridiculous--- they are always scrunched extremely close to the horizon, so they are unphysical in 't Hooft's brick wall picture, or Susskind's complementarity, so long as you come out after you came in, in brick-wall time.

The gluing picture is the only way I can make sense of the happy oscillations in AdS/CFT, which in terms of particle proper-time are oscillations through event and Cauchy horizons again and again and again. I don't see any other way to make sense of the picture.

Maldacena was famously confused on this issue in the 1990s, and tried to make a dual AdS space in the late 1990s probably motivated by the need to describe a maximally extended black hole. This proposal never made sense--- the single AdS space is what works.

Anyway, I look for the gluing from time to time, but not for a few months already.

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  • $\begingroup$ How is the classical description you give consistent with relativity; how can the particle cross the event horizon when by definition a particle would have to exceed c in order to do so? $\endgroup$ – user1247 Sep 3 '12 at 9:45
  • $\begingroup$ so in your point of view, there is really no chance for black holes connecting spacetime with nontrivial topology. Why is that picture so absurd after all? maybe the horizons really become entangled, and they neither shrink nor grow, because what falled in equated what get out on the other side $\endgroup$ – user56771 Sep 3 '12 at 12:56
  • $\begingroup$ @user56771: It doesn't violate relativity at all, please learn the maximal extended solutions. The particle is coming out the white hole part of the black hole solution. It is coming out of a past region in the extended solution. This is gluing the future to the past. The reason there is no chance to go into another universe is because it violates unitarity, and it can't be described as unitary horizon oscillations. This is well established. The picture I give is consistent with all that is known. $\endgroup$ – Ron Maimon Sep 3 '12 at 17:43

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