The Dark Shell (7) Basic Geometry

Assuming that the surface of the dark shell is a warped mathematical surface which permanently contains everything within it, a single event which created cosmic rays would, given enough time, result in a thorough mixing. This would explain their present random distribution. The lower thresh hold of energy for these would be of interest, in that below it, this random propagation seems to fail.

Assuming that the theory of constraint radius is correct in that compact dark matter surrounds each galaxy, out to a given radius as a function of its mass, then this relationship should also exist for baryonic matter at the atomic level. Thus a collision between two baryonic particles should be slightly proceeded by the impact of their respective surrounding shells of compact dark matter. Further, as the resulting mass is greater (doubled if the particles are of the same mass), the resulting temporary mass would have a larger constraint radius. Relativistic considerations aside, assuming that the resulting mass then fragments, the resulting constraint radii would be scaled to the respective masses of each of the final particles. This complex process may, of itself, affect the basic transition of the baryonic matter during such collisions. It is more likely however that this process is a passive effect for most transitions.

In general, if the theory of triple point singularities (each of which results in a big bang) is correct, then the spatial location of these should be somewhat adjacent to the remnant of the ultimate black hole. That is, they would be in regions in which the oscillation of the dark shell is greatest. This roughly should be at a maximum distance from the anchoring remnant of the ultimate black hole; that is, on the inner surface on the other side of the dark shell. However -- it would seem to be misleading to think of the dark shell in classical terms using regular Cartesian spatial references.

For some purposes, it may be convenient to speak of the structure in terms of a regular closed structure, however it is unlikely that things are so simple. Time should be substantially distorted on/at its outer surface and, as a result, a new type of geometry is probably needed to describe its actual configuration. The remnant of the ultimate black hole also probably plays a role in defining this new geometry. Further, if remnants of prior dark shells do festoon the outer, and perhaps the inner surface, of a dark shell, then these further complicate the situation. Such remnants should tend to be rather stable and additionally may relate to the formation of triple point singularities when located on the inner surface of the dark shell.

The actual trigger for a big bang may be the entry and destruction of a black hole into a triple point singularity. If this is so, then it would seem that the absolute sizes of universes should vary greatly. If however they are all about the same size, then perhaps as the singularity reaches some given size it either triggers because of its size or because there is then a surge of matter into it due to other effects.

It would seem that the warped boundary of the dark shell should share some of the attributes of the surface of the original ultimate black hole. In some fundamental sense however, this boundary is probably abnormal and distinctive. Actually in the normal sense of what a boundary is, that is a region separating at least two different categories of matter and/or void, there is probably no true boundary at all. The warping may avoid the need for such a boundary (to permit/define/allow containment).

A new geometry which effectively describes the outer limits or boundary of a dark shell should map back into or onto the surface of the original ultimate black hole. This special original layer would be thin compared with the bulk of the dark shell and it would seem logical that some of the attributes of this special layer would also be found in the characteristics of the boundaries of the dark shell. It might be best to think of this special layer as a type of planar singularity which maps out and forms the limits of the dark shell.

Arguably, the environment of the initial transition event with which a big bang begins, may be very similar to the steady state condition of the interior of the original ultimate black hole which formed a dark shell. The final condition of the interior of the remnant of the ultimate black hole may be quite different from the original ultimate black hole. However given the great mass of the remnant, these final conditions may be almost identical to those of the original ultimate black hole from which it evolved.

If the creation of triple point singularities arises from oscillations of the dark shell and if the irregularities in a dark shell, particularly those arising from the collapse of portions of a previous dark shell onto the new dark shell, are necessary, at least in part, for the creation of these singularities, then the first dark shell to have been created would have to have been sterile -- producing no singularities (and no universes). The first collapse and regeneration of the dark shell would have been a prerequisite to the creation of singularities.

Assuming that our (original) ultimate black hole (which formed our dark shell) was as large as the present universe, the relative mass/energy of our universe is trivial in comparison, given the very low relative density of our universe.

The creation of a rogue singularity requires comment. It would seem that an unusual situation would arise if two or more singularities were created in close proximity to each other. If the conditions were ripe for the creation of one, then perhaps more than one -- even a string of singularities, might be created. A factor which might be critical in the creation of a rogue singularity which destroys a dark shell may be its location, as some region(s) of a dark shell may be more vulnerable than others.

Hereinabove it has been postulated that a dark shell creates singularities while a portion of its surface moves away from its center. Given the great size of the dark shell and the substantial variations in its surface as well as the complexity of its motion, it could well be that singularities are also created when moving the other way. Since it is unclear what the spatial relationship between a singularity and the location of its resulting big bang might be, it may be that some or many of the big bangs occur within the structure of the dark shell itself. In such case, these should be considered as aborted given the proposed rather irregular and unfriendly environment of dark shells.