If a perfect diamond is placed within a small crucible-basket furnace
constructed of Tungsten wire ( in vacuum ), and the wire is raised to a
temperature of say T = 1200 C, then the Tungsten wire glows intensely (it is
"white hot"). However, the diamond within and in contact with Tungsten crucible
does not glow at all!!!
The diamond crystal is an example of Hot Dark matter.
If an imperfect diamond (with internal lattice impurities) is placed in the
tungsten wire crucible, then radiation from the localized diamond imperfections
can be observed. The diamond is hot indeed.
The perfect diamond lattice, even at atmospheric pressures, has a very high
DeBye temperature (~1850-2200 kelvin) and a very large band gap (~ 5-7 ev). For
temperatures below the DeBye temperature, radiative electronic excitations -
that require a relative displacement between the center of mass and the center
of charge - do not occur. Sound can distribute the thermal heat energy within
the diamond lattice, but electronic excitations do not. The diamond and other
structures with a high DeBye temperature, such as sapphire, make excellent
thermal conductors of heat.
But now suppose that very large mass aggregates, under the influence of
very strong gravitational fields and their attendent high pressures, have
properties similar to that of the diamond lattice. Indeed, as pressure
increases it is known that the DeBye temperature of diamonds increases. Then
such gravitationally collapsed carbon structures, even though they may be hot,
would not be seen, for in effect they do not radiate. Question: Are there
massive (carbon?) star stuctures in the Galaxy that are hot, but do not glow.
Are such "diamond stars", which do not radiate, the source of dark matter and/or
what might appear to be "black holes"?