Colored holes & droplet singularities
A massive star ends its career as a supernova where most of the mass it expelled into
the interstellar medium. The central core of the star is usually compressed to a very dense
neutron star that resembles an atomic nuclueus but has a radius of about 10 km
and a surface gravity of several billion g-forces.
Increasing the mass of such neutron stars somewhat could cause objects known as
gray holes where the gravitation is so strong that the surface of the neutron star
resides inside the photon orbit and only light that is emitted at angles larger than
the tangential plane can escape from the star.
When this angle becomes orthogonal to the surface (if not sooner) the nuclear forces can
no longer withstand the gravitational force and the star collapses to a black hole.
In reality a very massive star never forms a stable neutron star but collapse directly to a
black hole, there may be cases however where two neutron stars collide with each other.
As the matter of a neutron star is compressed the nucleons merge to form a quark-gluon
plasma and when this is further compressed GUT interactions involving ' X-bosons ' become
involved.
The classic solutions of general relativity predicts that all the mass will end up in
a pointlike singularity (it is often stated that rotating holes have ring-shaped singularities but
these are only artifacts of unsuitably choosen coordinate systems)
As one considers the effects of quantum theory it is evident that new physics will have to
emerge at the Planck density (of 10^76 GeV^4) this is the energy scale at which
Heisenbergs uncertainty principle would allow objects to spontaneously form in vacuum
that had a Compton wave length equal to their event horizon.
Such objects are called virtual black holes but the actual quanta of the microcosmos
must be regulated within a field theory of elementary particles.
In the context of string theory such elementary quanta would have masses that could be
0, 1, 1.41421, 1.73205 ... sqrt(n) times the Planck mass.
One possibillity could be that the singularity of a black hole settles down as such a string
state of very high excitation level.
Another more realistic (?) alternative is that the interactions of strings that are compressed
to a higher and higher density would give rise to balancing forces and a stable objects would
form dependending on the equation of state for such a
string soup .
For an example of such an equation of state one could imagine that the mass 'm' of the individual
strings equals the 10'th root of the mass 'M' for the entire black hole (in Planck mass units '10^19 GeV').
The density of the string soup droplet would be 'm' to the 4īth power (in Planck density units
'10^76 GeV^4') and the volume of the droplet would have a radius equal to the 5'th root of the 'M'
(in Planck length units '10^-35 m').
Mass = density * volume (m^10 = m^4 * m^6) ; Volume = m^6 ; Radius = m^2 = M^1/5
As an example a stellar size black hole with a total mass of 10^40 Planck masses would
have a singularity with a radius of 10^-27 m and the number of strings would be 10^36 each
of those would have a mass of 10^23 GeV.
Apart from the singularity the large scale structure of a gravitationally collapsed object
is perhaps not as well established as one could think.
The characteristic property of a black hole in that it has an event horizon is really
not so very straightforward. This event horizon at a radius of 2M is dependent on the existence
of a Killing vector that is no part of Einsteins equations as such but is added as an extra
ingredient to simplify the solutions.
This business concerns the deeper issues of general relativity where the axiomatic foundations of non-euclidean geometry in the form of Lie derivatives and their associated groups
has to be accounted for.
One alternative solution to curved spacetime is a red hole where the photon orbit has decreased
from 3M to 2.718M and the event horizon has shrunk from 2M to zero.
Perhaps in a TOE where gravity is joined with the other interactions in some framework like
the transhyperbolic group a collapsed object would best be descibed as an
INFRA-RED HOLE that would have a photon orbit and
event horizon smaller than that for a standard BLACK HOLE with the natural log
value for the photon orbit and the vanishing event horizon of a
RED HOLE as the extremal case.
Such a scenario would be an interesting parallell to the Lamb shift in atomic physics
that causes a small deviation from what would otherwise be integer values when measuring
the magnetic moment of the electron.