5  A more detailed analysis of a Rotating black hole inside its event horizon

 

     5. 1 An overall view of the collapse process

 

Firstly let us assume for simplicity that the angular momentum is (slightly) less than the absolute maximum that the mass of the hole may contain and that no further matter or radiation are coming into the hole.   The gravitational collapse continues inside the event horizon.  The initial collapse will continue, the particles will interact and the material will heat up further.  Let us assume that it is rotating as a fluid body and eventually the outer surface will be rotating with a velocity approaching that of light at the equator and this cannot contract further.  Particle interactions will then cause the angular momentum to be shared out and the inner particles will gain more angular momentum and it will settle down to a toroidal structure heading towards the theoretical "ring singularity" as described by the Kerr solution to the equations.  (see  virial theorem)

 

It is unlikely that there is no residual angular momentum in other dimensions so as this settling down continues a toroidal rotation in one direction around the orbital axis will happen and the end result is likely to be a toroidal surface. Particles will be spiralling round the position of the theoretical ring singularity.   However a significant local change has taken place. There has been a change in the local dimensionality from spherical (3 dimensions) to cylindrical (2 dimensions) which means that the local gravity follows an inverse first power law rather than an inverse square law.  (see the appendix dimensionality of universes and conservation laws) this slows down any collapse allows more freedom of movement and will result in the particles oscillating about the theoretical ring singularity axis.

 

Now consider in detail what happens on the smaller scale as the collapse continues.  As the temperature rises, collisions between particles will become more violent and particle antiparticle pairs will be created.  This will in effect drain energy and angular velocity from the system by converting it into mass and reduce the temperature rise. The increased mass will also allow the torus to collapse to a smaller diameter thus releasing more gravitational energy. 

 

Electron pair production cooling processes are already accepted already as the process driving some rare exceptionally violent large supernovas. (Hypernovas)

This means that the collapse process will create a lot more matter and antimatter.   The collapse process will also gradually cause a cooling down of the temperature as the particles and radiation settle down to their orbits the energy differentials reduce and the mean free time between collisions will increase.

 

So far there is one big omission in this analysis and that is the effect that all this is happening with the particles moving in orbits at relativistic velocities and the effect of frame dragging or gravitomagnetism.    The image of highly relativistic particles and radiation orbiting in spirals around the final ring singularity creates an image very similar to that seen in a structure in the origins of Twistor theory that is the Robinson Congruence in the compactification of Minkwoski space  see   http://users.ox.ac.uk/~tweb/00001/ 

 

 

                  

 

The lines represent the way thew Minkowski null lines are bent and dragged around the collapsing Kerr black hole

 

One of the main analyses of the Kerr black hole shows a gravitational repulsion effect in some areas of the space around the ring singularity and this leads us on to the next question.

 

 

       5. 2  The Reversal Process

 

 

 

I understand from comments in other review papers there are some mathematical Physicists working on the problem of converting a collapsing system into an expanding "big bang".  Clearly this is a vital requirement for the concepts presented here to work. 

 

To clear up any uncertainty it is clearly not possible  whatever happens for the results to explode out of the event horizon because that is irrevocably sealed and limited by the physical laws in our or any other similar universe.  There are however plenty more dimensions available for expansion to occur because all main theories of everything have far more than the conventional three of space and one of time available to them.

 

           Matter- Antimatter symmetry  

There is a symmetry between matter and antimatter this could be caused by the geometry of the collapse,   To create an antiparticle from a particle requires a total reversal of the CPT properties of that particle.  That is an antiparticle is a particle of the opposite charge and parity travelling backwards through time. Now normal matter particles created in these particle generation interactions and travelling forwards through time are dragged in the direction of rotation by the frame dragging the antiparticles are driven in the opposite direction by the time reversal and forced to expanding the space like dimensions released from time by the event horizon forming.

 

   

         Local view of the particles and space time

This is a vital part of this thought experiment.  Relativity rules apply!  There is a strong tendency for people to visualise black holes as looking from the outside as if the event horizon was transparent this is bad thinking, it is important to consider what this "universe" looks like from the point of view of the particles involved as the space time collapses towards this theoretical ring (or toroidal) singularity.

 

Orbital motion implies that there is always a certain amount of coherency in the particle movements.  Initially the temperature will rise as gravitational energy is released and then “cool down” as particles are created and motions become more and more coherent,  The gravitational field and potential will become higher and particle velocities closer and closer to the velocity of light and particle interactions less frequent.

 

Although the particles are moving in a tight set of toroidal "orbits" around the theoretical tiny ring singularity orbit around the main centre of gravity,  From the point of view of the individual particles time dilation will mean that they will become more spaced out from their own point of view.

 

It is also important to consider the effects of the local "dimensional restriction" on the conservation laws.  The classic inverse square law requires the existence of three local dimensions. in a two dimensional situation such as infinite cylindrical geometry energy spreads as the reciprocal of the distance and conventional orbits are not stable and in a one dimensional situation for example above an infinite radiating plain energy is constant with distance  This is interesting as a uniform restoring force also allows simple harmonic motion as in orbits

 

Now the standard texts describe that inside the event horizon space becomes time like and time space like.  Roger Penrose with his Penrose diagrams of space and time considers the possibility of moving past "the singularity" to get to another universe like a wormhole.  Can I now suggest that we consider that the "time like" space collapses towards a linear or toroidal surface singularity to become time in a new universe  and the "space like" time expands to become space in a set of dimensions different from the space that has just collapsed.

 

It is now interesting to note that antimatter is often described in texts as identical to ordinary matter running backwards through time so it seems likely that our new universe could be dominated by what is in our universe called antimatter. 

 

 

          5.3 Dimensionality and Conservation Laws

 

 

3.1   The Dimensionality of a potentially metastable and long lived universe

 

This is an important paper on this topic

 The relationship between the dimensionality of a universe and its behavior are discussed in the paper

 “On the dimensionality of space-time”      By Max Tegmark   http://space.mit.edu/home/tegmark/dimensions.pdf

 

 

Abstract. Some superstring theories have more than one effective low-energy limit corresponding to classical spacetimes with different dimensionalities. We argue that all but the (3 + 1)-dimensional one might correspond to ‘dead worlds’, devoid of observers, in which case all such ensemble theories would actually predict that we should find ourselves inhabiting a (3 + 1)-dimensional spacetime. With more or less than one time dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions. In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures. A space with less than three dimensions allows no gravitational force and may be too simple and barren to contain observers.

 

      Additional comment

This concept is a vital trigger for the possibility of the matter - antimatter oscillation concept in the black hole evolutionary universe.  The important aspect of of CPT conservation is that a collapsing universe of matter by CPT transformation is turned into an expanding universe of antimatter.  The quoted description of Tachyons ( matter particles travelling faster than light)  is just another way of looking at antimatter.

 

  

5.3.2      The relationship between dimensionality and conservation laws

 

Noethers Theorem (QV)   demonstrates that symmetries define conservation laws notably  translational  and rotational symmetry require the conservation of energy and angular momentum respectively

 

Energy conservation laws constrain the laws relating to the forces associated with long range fields based on the local dimensionality.  The classic inverse square law for gravity and electric fields is because we live in a universe with three spatial dimensions because the surface area of a sphere around a point increases as the square of the radius.  This defines the way the radiated energy is spread out as one moves away from the point source.  I have used the term "local dimensionality"  because most root cosmological theories envisage larger numbers of dimensions (possibly infinite) at the most fundamental levels of the bulk from which universes originate.

 

This can be seen in the cases of pseudo restricted dimensionality. For a source which is an “infinite” line we have only two local dimensions  and the energy is spread over the perimeter.  This becomes a simple inverse law and for an infinite plane flat surface radiator this spreading becomes a constant because the energy does not fall off.   This produces the reciprocal relationships in string theory.

 

Expanding this concept to more than three dimensions implies that the fields fall off as the number of dimensions less one;  for example, the case of four dimensions results in an inverse cube falloff of force with distance.  Inverse cube and higher laws do not allow stable orbits to form although other sorts of resonances may be possible.  As the dimensionality gets higher the and the inverse power laws related to force get higher the tendency to collapse to a singularity or a lower dimensionality becomes greater if there is any disturbance on total uniformity.   In all cases total uniformity is an unstable equilibrium and any disturbance causes expansion or collapse.

 

The inverse square law is the only one that allows reasonably stable orbits to form.  Any variation from this results in collapse or breakup of an orbit with the slightest disturbance from its metastable position.

 

 

  5.3.3  The "relativity" of dimensions.

 

There is a strong tendency to consider our dimensions of space and time as sacrosanct and immutable.  This I believe is a mistake they are local properties of our universe and do change as event horizons are crossed where space becomes time like and time expands and becomes space like.  On needs to free one's thinking in this respect and think of dimensions more in the way that communications and information theory treats them. 

 

As in Einsteinian Relativity of time and space dimensions are themselves relative so new dimensions can expand without interfering with dimensions that collapse.

 

 

Please note particle antiparticle asymmetry  is an important symmetry breaking that has only recently been discussed properly in the standard theory of the development of our own big bang but is now observed in high energy physics experiments.

 

This could now represent a process similar to our observed big bang however the process has also been "seeded" with particles from our universe and although there may be changes on physical laws,  There will be restraints caused by this seeding.

 

After this collapse process has happened, further material may fall through the original event horizon  but it will appear only as a small number of extremely high energy (antimatter?)  particles in the vast new universe that has in effect expanded from the small amount of matter that first created the "singularity" in the black hole. This may result in one of the potentially observable confirmations of these concepts.

 

          5.4  looking at this from a different direction

 

Let us assume for the moment that this evolutionary cosmology is true and the creation of our matter universe was driven by the collapse of a stellar mass black hole in an antimatter universe and that this collapsing antimatter universe existed in the moment NOW in the two compactifed complex dimensions of time in our universe.  This means that every electron or quark that was created in the energy release by the collapse has its antiparticle partner in this compactified structure 

 

The moment NOW is a tiny but finite time period and eventually as the collapse cools by matter antimatter creation Initially this collapse is under an inverse square law and is very fast giving a vast release of energy but as the structure gets closer and closer towards the ring singularity the energy release gradually changes to a logarithmic process that still has a theoretically infinite final energy but the process becomes much slower and is probably still continuing and may well have some relationship to the increasing expansion of the universe. as could matrrial falling into our originating black hole.

 

 

On to 6 Towards an evolutionary process