🚀 go-pugleaf

In article <80722@ut-emx.uucp> johncobb@ut-emx.cc.utexas.edu (John W. Cobb) writes:

>Most (All that I have ever seen) "no-hair" theorems are proved for classical
>systems. What about quantum systems? If a true quantum description of Hawking
>radiation (not just a semi-classical estimate) is finally worked out, is
>it not possible for it to depend on "the hair". for example, if a proton/
>anti-proton pair is created out of the curvature field just inside the horizon,
>will both the proton and anti-proton have exactly the same probability to
>tunnel beyond the horizon? Might not these probabilities be affected by the
>overall baryon number of the black-hole. Perhaps this is a way to restore
>baryon conservation in collapse situations --- then again, black holes may
>not respect baryon numbers, even in a complete quantum description.

A couple of weeks ago I posted a reference to an excellent expository
paper on this subject.  Unfortunately I no longer have the reference on
me.  Maybe someone can mail it to John Cobb - this reference is what
contained the business about "if you throw an encyclopedia into a black
hole, can you recover the information from the Hawking radiation
emitted?"... leading to many jokes here on sci.physics.  The paper
is available electronically from hepth, the high-energy physics
preprint service.  

In any event, at least in toy models quantum black holes can have
hair.  In 4 dimensions quantum gravity is too hard for us to know yet,
but people who have taken the trouble to learn string theory have
developed a lot of expertise in 2-dimensional physics, and in particular,
one can supposedly exactly solve the quantum black hole in 2 dimensions
and look for hair.  I.e., look for more quantum numbers.  They find
them, so quantum hair is a hot topic.  As you point out, this relies on
a true quantum description of the black hole, not a semiclassical
approximation in which the gravity field is treated classically and the
electrectromagnetic and other fields are treated quantum-mechanically.
(Hawking makes yet another approximation, treating the shrinking of 
the black hole due to the radiation adiabatically, i.e., not studying
the effect of the shrinking on the radiation in detail.)  

So there is some room for hope that a true quantum description will
restore baryon number (or other better quantum numbers, like lepton
number) conservation.  However, the author of this review paper gives
reasons why he thinks quantum hair will not save the day.  They are nice
but hand-wavy arguments and I am a bit too tired now to recall and
explain them.

In any event, I would think the key thing in this business would be
to see if FOUR-dimensional black holes can have hair when treated
quantum mechanically.  I'm not asking for much here - only a fully
working theory of quantum gravity.  :-)  Until we get one I don't
see how to study these questions with any assurance of being right.
Experiment is out, alas.