4 The Continued Collapse inside Black Hole

The first and most obvious question to answer is, could a universe as large and complex as ours come from the collapse of a stellar mass black hole inside its event horizon?

It is accepted that the basic physics does not change as the event horizon is crossed and locally there are no significant changes other than the increasing gravity gradient. Also the high energy physicists have shown that at conditions similar to those only nanoseconds from the start of the big bang the physical laws are still stable we can pursue this model much further

Let us then consider the collapse of material inside a stellar mass black hole starting immediately after an event horizon has first formed.  Let us initially consider the simple Schwarzschild or non-rotating and balanced charge case .  It is accepted that this case is not realistic as all black holes are likely to have rotational energy and considering the amount of collapse and compression before they form this is quite likely to be near the maximum

Inside the event horizon the collapsing material is extremely hot and turbulent and will continue heat up as a result of the release of gravitational potential energy being turned into kinetic energy.   As it collapses further the gravitational field continues to increase as the inverse square of the radius. 

Let us consider the collapse of a spherical shell of mass from radius r to r/2.  Simple mechanics shows that an individual particle at the surface of this shell will gain energy in proportion to the reciprocal of the radius change  ie 1/r  as the radius change is r/2   the value of the radius disappears!  that is a constant amount of energy is converted from potential to kinetic energy for every halving of the radius of the collapsing mass.  This will tend to infinity as r approaches zero.  So the total energy confined within the event horizon heads towards infinity.

This collapse is over a finite distance and takes a finite time. but the conditions under which it takes place allow the particles to have a vast number of interactions while it takes place.  It follows that in the collapse of even a small stellar mass black hole there is therefore plenty of energy available to create a whole new universe as large as or even larger than our own observable universe.  There is also sufficient time for particles to interact and multiply by pair production as the temperature rises.  Note the creation of new mass by pair production will also increase the gravitational field and cool the the collapsing mass.  With this amount of energy available inside the event horizon any subsequent material falling into the black hole after the initial collapse event has taken place is largely irrelevant and will be discounted at this stage of the story.

Mathematics clearly states that once the event horizon has formed, the matter inside a non-rotating black hole collapses to a mathematical singularity of zero dimensions containing an infinite quantity of energy within a finite time.  This is clearly very bad physics and does not make sense in the real world but it is what all the textbooks say and most people accept.  Essentially I see this as a way of saying, something must happen but we have no idea what!  I have been unable to find any analysis of what might be an attempt to work towards real physical solution to this by analysing this collapse in detail as far as our current understanding of high energy physics allows but  I will offer you a simple and fully plausible one based totally upon accepted physics now. 

Let us assume we have a body collapsing under gravity in empty space and forming a black hole.  Let us assume that no other particles or radiation are entering the hole.

Consider the instant that the event horizon forms.  This is the moment that photons cannot escape "to infinity" however particles will be interacting at the collapse surface and radiating photons and particles in all directions.  Photons and particles created by interactions close to the surface of the collapsing mass can always escape some short distance from the contracting central mass before being dragged back into the main body of matter.  The photons will travel the furthest.  Let us call this limit the "photon sphere".  This is known as the last stable orbit for photons around the outside of the actual event horizon.  In this case as there is no stable orbit the photons will just fall back into the collapsing mass.

The collapsing mass will be inside this "photon sphere" although the particles will be travelling at speeds quite close to the velocity of light so this will not be very much inside this limit.  As the mass collapses the "photon sphere" will retreat inside the event horizon and represents a sort of second "event horizon" defining the limit of the radiation from the collapsing mass. This is in fact just the same as the second event horizon inside a Kerr black hole As the gravitational field increases this photon sphere will contract with the rest of the mass.  Between this and the real event horizon in our universe superficially there is absolutely nothing other than the quantum mechanical vacuum as long as no matter or radiation is falling into the hole.

Now this Photon sphere may represent the “firewall” inside a black hole that recent quantum studies have talked about but the important thing it is not as you initially cross the first event horizon to infinity but much deeper inside the structure.

Now is there absolutely nothing between the event horizon to infinity and the firewall?    It is currently accepted that the event horizon of a black hole to our universe radiates energy in the form of Hawking radiation and that this can cause black holes in totally empty space to decay very slowly to nothing.  The total energy radiated is proportional to the gravitational gradient at the event horizon. (see ref below) This energy loss is incredibly small for all gravitational gradients that we can expect to encounter in our universe.  However as the gradient increases it increases without limit.  That is, a gravitational gradient radiates energy away from a gravitating source into its photon sphere.

This result implies that the photon sphere of material collapsing inside the event horizon of a Schwarzschild Black Hole will radiate energy in proportion to the gravitational gradient at its surface.   This radiation will of course eventually fall back into the hole but it will take some time doing it, let us call this time the "return time".  

The rate of energy loss over the return time is in effect a drain on the total energy in the hole.   As the main mass continues to contract towards the "singularity" and the gravitational gradients increase further this energy loss rate will increase as the inverse square of the radius  (source https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator  )  The energy gain by the collapse as worked out above increases only as the inverse first power of the radius.  This means that the energy loss would eventually overtake the energy gain from further gravitational collapse and the structure will become a stable (tiny) radiating fuzzball with an incredible but non infinite quantity of energy.  

 Again using  https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator  and inputting that the radiated energy should be around  10e20 solar luminosities to approximately equal that of the whole observable universe comes out with the result that the radius would be around the Planck length.  However small this is still vastly bigger than the infinitesimal size of a mathematical point.  It may also be the starting point for our first and most important constant, the constant of quantum mechanics itself, the Planck constant.

The non-rotating black hole is of course also a mathematical simplification.  All black holes will contain some angular momentum and follow the Kerr structure.  This approach will be the start of the next stage of the argument.

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