From: utzoo!decvax!yale-com!leichter
Newsgroups: net.physics
Title: Re: Black Holes
Article-I.D.: yale-com.363
Posted: Fri Nov 19 17:44:12 1982
Received: Sat Nov 20 04:26:11 1982
References: sri-unix.4177

The radiation seen "coming out" of a black hole, in Hawkings' theory, is
carefully worked out.  It turns out that a black hole is also "black" in
the thermodynamic "black body" sense; it is a radiator with an equivalent
temperature.  The temperature turns out to be proportional to 1/A, where
A is the area of the black hole; "area of what" needs careful definition.
(It's of the sphere at the Schartzchild radius for a non-spinning black hole,
I'm pretty sure.)  Now, a black body is a RANDOM radiator; any combination of
particles with a given energy is as likely to be radiated as any other.  Hence,
given enough energy, a TV set COULD come out - although it's very, very
unlikely!

The radiation caries away energy, hence masss; so the black hole gets lighter.
The area shrinks, all other things being equal, as the mass goes down.  But
this means the temperature goes up, implying more radiation.  So the actual
radiation pattern you see is a gradual but accerlerating increase; the black
hole eventually vanishes in a burst of gamma rays.  (In fact, if there were
small black holes created in the big bang, we should see gamma ray bursts
from their collapse.  We don't.  This implies that there could not have been
to many black holes of such a size that we'd see them exploding now.)

Note that when a black hole explodes in this way, NOTHING is left - you do
NOT get the original object back.  It's wrong to try to extend your normal
view of the world "into" a black hole.  A black hole is TOTALLY specified
by just three quantities:  mass, charge, and angular momentum.  It is im-
possible to determine anything about what went into the black hole other
than that the total of such things gave those three numbers.

It turns out that, if you take a black hole with a given mass, charge, and
AM, and calculate the set of all particle configurations that could have
collapsed to give that black hole; and consider that you have lost the in-
formation that specified which of those configurations you started with;
and hence have increased entropy by that amount; you can calculate an
equivalent temperature, thermodynamically, for the black hole.  You guessed
it - the result is the same as for the calculation done the other way
(calculating the probabilities of all virtual particle pairs that could form
near the black hole and have one of the pair disappear into the hole while
the other radiates).

I should note that the equivalent temperature of a black hole of any
reasonable mass is tiny.  If I remember right, a black hole with the mass
of the sun would have an equivalent temperature of 10**-4 degrees absolute.

Finally, one point that is often missed is the distinction between black
holes and singularities.  The General Relativity field equations place some
constraints - which are very tough to evaluate in detail - on what the space-
time "fabric" can look like.  They allow for singularities - places where
the usual metric structure breaks down.  A singularity is not a black hole -
rather, it is a region of space-time of a particular form that SURROUNDS a
singularity.  Such a singularity is "nice" because it is shielded from view
by the black hole - we can never observe the really crazy things that can
go on in the region of a singularity - physical laws just break down.  A
"naked singularity" - one we could actually observe - would lead to all sorts
of problems for our world-view; causality breaks down, for example.  Hence,
most physicists believe that the field equations do not allow a naked
singularity.  However, the last I heard, no one had proved this.  (I think
it is known that the only spherically symmetrical singularities are inside
of black holes.)
							-- Jerry
						decvax!yale-comix!leichter
							leichter@yale