Re: More "No Hair"

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Jim Green asks:
> But now I have another question: what other types of Black Holes *could*
> there be????  I mean after everything is stripped apart and squished down to
> a solid mass of quarks or whatever things quarks are made of, what other
> characteristics *could* there be beside mass and spin?????

The whole (pun here) point of the 'no hair' theorem is that *isolated*
black holes have very little in the way of properties.  They are *not* 
'made' of any substance (no solid mass, no quarks, no quark parts, nothing
at all).  If a black hole was built up out of 'stuff' then it would possess
the particular properties of it parts.  A black hole is a classical static
empty spacetime solution of the equations of general relativity which has
a region of spacetime characterized by a singularity and surrounded by an
(event) horizon.  Any matter that was used to form the black hole in the
first place would have been lost to the singularity which ate it.  The hole
is sort of the Cheshire cat grin left behind in spacetime after all the
matter has been crushed into (destroyed at) the singularity.  The reason
that 'mass (or energy)', 'momentum', 'angular momentum' and 'electric
charge' remain is that only these properties by themselves leave their mark
on the structure of the singularity and the spacetime around it, and since
they are (locally) conserved--even in general relativity--there is no place
for them to go and no way for them to disappear during the formation
process (in an asymptotically flat spacetime with localized matter).

Since there is no known mechanism for creating the huge charge separation
that would be necessary to make a black hole with a significantly large
electric charge ('significantly large' here means large enough to
measurably perturb the spacetime around it away from the uncharged case) we
think that we do not have to concern ourselves with (significantly) charged
black holes.  Also, since the total momentum and orbital angular momentum
of the black hole can be defined away (for an isolated black hole) by
simply observing/describing it from a convenient frame of reference, (i.e.
one for which the hole is at rest and centered on the spatial origin) we
are left with just the properties of mass (aka internal energy, oops, I
shouldn't reopen that debate) and spin (aka internal) angular momentum.
These are the two properties that Hawking was talking about in the quote
that Jim gave about the 'no hair' theorem.  (If it ever becomes verified
that isolated magnetic monopoles exist, then it is possible, in principle,
that a black hole may also possess the property of "magnetic charge"
besides the other properties mentioned here.

If a black hole is not isolated then more interesting things can happen.
Time dependent gravitational radiation emissions, coalescence behavior
during black hole collisions, black holes mutually bound in decaying
orbits, etc. are interesting possibilites.  Also, when quantum effects are
turned on, other time dependent effects (such as Hawking radiation) can
occur.

Brian Whatcott speculates:
> Since you asked...I will unashamedly speculate.
>        
> Translational velocity ( else there is an absolute reference...)

Certainly a black hole will translate with a net velocity and total momentum
when it is observed from a frame in which it is not at rest.  I don't
understand the parenthetical phrase above though.

> Temperature?

Yes.  Once quantum field theoretic effects are included in the spacetime
region near a classical black hole's horizon, one finds that Hawking
radiation is emitted which is characterized by a black body temperature.
It should be noted that the temperature is not another separate independent
property of the black hole.  The temperature depends on the proper surface
gravity at the hole's horizon, which itself is entirely a function of the
mass and spin angular momentum of the hole.  The other thermodynamic
properties of the hole are also determined by the mass and spin angular
momentum.  For instance, the entropy is directly proportional to the
proper area of the horizon, but that area is a function of the mass and
angular momentum.

> Viscosity ( of various kinds ) ??

Nope.  No single black hole has any viscosity property.  (Maybe a gas-like
swarm of gravitationally interacting micro-mini black holes may possess 
a GR version of the statistically emergent property of viscosity.)

> anisotropisms of the integrated energy emissions??

Such an effect is entirely a function of the net spin angular momentum and
the mass.

> Spectral waveform of the aforesaid emissions?

This is a function of the temperature, which as said before is a function
of the mass and angular momentum.

> Charge?

Its possible in principle.  It is difficult to see how in practice a
significantly charged black hole may be formed.

> Magnetic field?

Not really.  An isolated uncharged black hole may not possess any magnetic
field.  This is because when the hole formed, the magnetic field (due to
the charge current sources in the matter) was swallowed by the singularity
together with its sources.  If a black hole had a net spin angular momentum
*and* a net electric charge, (such as is described by the Kerr-Newman family
of metrics) I guess that the black hole would then have an associated
magnetic field.  I suspect that Paul Camp would know more about this specific
case.  In this case the magnetic field value throughout the spacetime region
in the vicinity of the hole would not be independently determined.  The whole
field everywhere would be a colateral function of the values of the hole's
charge, angular momentum, and its mass.  If magnetic monopoles are allowed to
exist, then a black hole may *in principle* possess a net magnetic charge.
If so, then it would then have an associated net exterior magnetic field.

> Unforseen effects of strong and weak nuclear forces???

Nothing we know about would work.  Of course, if an effect is unforseen
then it can always pop up without permission.  If effects from other
nongravitational interactions (such as the strong and weak forces) did show
up, then they would have to have showed up through intrinsically quantum
effects.  For such a situation the classical black hole solutions of GR,
and even GR itself, would need to be superseded by solutions from the
appropriate quantum gravity-including theory of everything.

David Bowman
dbowman@gtc.georgetown.ky.us