I think that nature has ways to avoid singularities. E.g. the two flows of air above and below an air foil, the section of a wing in an aircraft, have different speeds at the end tip: faster above than below: then viscosity enters into the picture and vortices appear to remove the "mathematical" discontinuity. Same happens when we have a supersonic flow that has to stop due to the presence of a solid object: then a shock wave is produced and the flow behind the shock is subsonic and no discontinuity appears. In the case of the initial stages of the universe, dealing with a theory with continuous variables like general relativity, we arrive at a "mathematical" singularity. Then quantum mechanics enters into the picture ad no singularity is in the picture. I believe that in nature there are no zeros nor infinities, no singularities. Nature is already "defined", and we have to understand it. Nature does not necesarily has to  follow our mental constructions.

It seems that both Big Rip and Big Bang singularities can be removed in string theory. For example, if we construct our universe in string theory, we can predict all future events.

To explain the universe as we see it, with large scale inhomogeneities in the background radiation, one needs inflation, that means, a mechanism which gives a''(tau) > 0 in the early universe.  Such a mechanism can, in principle, also prevent the singularity. 

If the mechanisms which are assumed to give inflation today are able to do this I don't know. For a theory of gravity which prevents the initial singularity see http://arxiv.org/abs/gr-qc/0205035

Perhaps this 1939 article by Oppenheimer and Snyder will help:

http://journals.aps.org/pr/pdf/10.1103/PhysRev.56.455

Plz study LQC models 

Dear Victor,

I reckon that some theories with varying physical constants can remove many kinds of singularities such as Big Bang, Big Rip and other, exotic singularities. The question is of course with the correctness of those theories and whether such constant as speed of light (which is dependent on the chosen units) can vary in some consistent way. If interested, please see the attached paper.

All the best,

Lukasz

One way to get rid of the initial singularity is to replace it with a connection between our universe and Something Bigger.

The problem with doing this is that if our universe is an offshoot of a larger system, then since all the information required to define that larger system won't by definition, have passed through the connection into our universe (because if it had, our universe would be the sole inheritor of that system's data), we're slightly at a loss to describe what it was that our universe might hypothetically have been an offshoot of. The connection might have been so small that we could have just inherited just a limited set of fundamental constants.

In that scenario, there's no real singularity, but frustratingly, we're unable ... on principle ... to extrapolate through the big bang to work out what came before. There's not enough inherited data to do the extrapolation. 

I also rather like the "Hawking Bubble" model in which there's an initial and a final singularity (Big Bang and Big Crunch), but in which these two points exist on a smoothly curved surface, so that they're merely coordinate singularities (like the Earth's poles), not geometrical singularities. In a Bubble model, if you extrapolate a path back through the Big Bang region, the line doesn't hit a dead end or emerge into another universe, it arcs round and reappears in another part of our universe, pointing in the opposite direction. Physically, it's still a Big Bang model, but there's no geometrical breakdown.

For a hypothetical geodesic of a particle plotted back towards and through the polar region, we can treat the combination of the two emerging paths (each eventually holding a particle), as describing a particle-pair-production process – although in this case, the particles aren't capable of forming until the universe has expanded and cooled somewhat.

Initial geometrical singularity can be removed by introducing a "Unified field of consciousness" as discussed in following two articles.

Article Unified field of consciousness

Article Periodic quantum gravity and cosmology

@A. Sepehri, Ilja, Rodney, Vahid, Vikram, Eric: thanks for your comments.

@Lukasz: thanks, where is your paper? Best wishes

Dear Victor,

Singularities are the result of mathematical models of matter more than physical. Only a correct physical - mathematical model can eliminate the singularities. I believe the problems of singularities in cosmology will be eliminated when we have a correct quantum gravity theory.

All the best,

Ion S.

Dear Victor,

I thought that RG has attached the link. The paper is on the arXiv: http://arxiv.org/abs/1207.4038

Regards,

Lukasz

In some models of the universe there is no initial singularity, some model has big bang singularity. All are based on theoretical basis.

Dear Victor,

Here you can check a McGehee regularization of the big bang. This technique has proven to be very useful in some common spacetimes such as the schwarzschild and Reissner-Nördstrom spacetimes:

http://arxiv.org/abs/1205.1474

Regards,

Pablo

Victor,

The model of the universe with the singularity called the big bang is only theory.  It is not even the most plausible one but it is the one that is most excepted. 

I do not think it is correct.  So my answer is there should not be a singularity at the beginning of the universe so it can be removed.

Our model of the universe has been this way sense about 1928 or so when George Lemaitre convinced Albert Einstein that it could have happened that way.  He used Alert Einsteins field equations of general relativity to show that it was mathematically possible.  There was then and still is not any real evidence that that is the way it was but we continue to build on the model as if it is correct. 

If it were the universe would look much different than it does today.  Our universe is way to consistent to have had such an explosion at the beginning and look this way.  Ask any Engineer that works with explosives what it would have to look like and they will tell you that this did not happen. 

It would take more mass and energy than the system had to make that happen and as far as I know there is no magic in the universe so that could not happen the way the theory states it did. Now if you want to slam a mass that was as big as the one at the center into it at a force that would have to be faster than the speed of light then you may get it outside the event horizon or Schwarzchild radius.

The real evidence is in the calculations of energy and the understanding that we should have from the Schwarzchild calculations that set up what a black hole would have to look like.  This should have stopped the argument from ever happening.  Schwarzchild calculated the distance at which a mass could no longer support its own structure and would fall into a singularity.  It was not called a black hole until much later. 

From this we should be able to calculate that if all the mass and energy in the universe were in one place at one time, no matter how fast it was rotating it could not have enough energy inside to push the mass out side the Schwarzchild radius. 

Also if it were rotating the universe would not look the way it does today as well.  Refer to an explosive engineer again for the look.  All we have to do is look into the sky and see how many things are spinning to say the chance that it was not spinning is almost zero. 

So there are somethings about the early universe that we could deduce from the conversation here.

The early universe was more than likely spinning or had some type of rotation to it.

It could not have exploded the way it was said to have in the big bang or it would look much different.  More like a shell than a uniformly spread out system of galaxies.

As we look at more and more galaxies we see that there is what we would call a black hole at the center of almost all of them that are spiral.

The vast majority of the galaxies we see are spiral in nature or have been blended together with more than one spiral galaxy.

If we look that the order of discoveries from the beginning of the last century to today we can totally understand why we think the big bang is correct.  But if we look at all the discoveries and change the order of discovery the big bang does not make any sense.

Also the uniformity of the back ground micro wave radiation is way to uniform to be from the big bang and can be seen as something else and is by some.  Yes there may be left over radiation if the big bang happened but it would vary a lot from region to region in the universe.  The more likely situation is that the back ground radiation is a much more local event or a galactic event and not the echo of the big bang.

However I have only been studying history and cosmology for about 40 years on and off and there are many more well rounded people that I would love to hear from.    

The history of all of this came to me some 15 years ago and I just did not want to give up on the big bang as I liked it too, but I realized how bad the science was.

@Ion, Lukasz, Haradhan, Pablo, George: thanks for your answers.

@George: it is very interesting you remark about rotation in early universe. In this regard, last year i published a paper discussing Primordial Rotation etc. If you wish, it is  available in this researchgate.net or you can search at www.prespacetime.com. Best

Victor,

Thanks I will look at the paper. 

This has been a passion of mine for many decades and my work has circled back around to give me deeper insight into the workings of the atom and then on to better understanding of the universe.  There is a direct connection with the very small world of sub-atomic physics and the ultra-big in the universe.  When we have competing theories that do not match there is something wrong.  I am slowly seeing that this is coming to light in my work.  

In 1976 I published a paper in Foundations of Physics (Vol. 6, pp. 59-63) proving that any initial cosmic state whatsoever will evolve in finite time to a universe that is expanding under a Hubble-like constant. I also presented the paper at a meeting of the APS. It was the only paper at the meeting that the Los Angeles Times did a story about. This infuriated the APS because the intermediate vector boson had just been discovered, as if the general public would understand and care about that. Because of the newspaper article, I got a nice letter from the late Carl Sagan who liked my paper. Proofs of theorems and the appreciation of celebrity scientists will buy you a cup of coffee at Starbucks if you have $1.50. 

Influence of Infinitesimal Neglected Effects by Current Theory of Gravitation and Experiments on the Stability of the Universe

http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50109

Abstract:

From the hypotheses compatible with microphysics theory, this paper establishes a new theoretical model of static universal gravitation and deduces new formula of the theory of universal gravitation. In a first order approximation, the new formula shows the inverse-square law consistent with Newton formula, which would indicate that the new theory is consistent with the experimental results that can be reasonably explained by the current theory of gravitation. The parameters and higher order terms among the coefficients of this paper reveal the numerous infinitesimal neglected effects by current theory and experiments. In the first order approximation, the meanings of the physical parameters included in coefficients are analyzed and the infinitesimal neglected effects are applied in the study of the stability of the universe, which overcomes the difficulty of singularity in the cosmology of Newton, Einstein, etc., and concludes that the boundary of universe is unlimited, without any need of the hypothesis that the universe starts off with the big bang. Therefore, this paper establishes a harmonious and ingenious relationship between microphysics and macrophysics theories. In addition, through the analysis of the formula derived from the theory of this paper, it is found that: in general, the gravitational constant is not always a constant in the gravitation formula requiring high precision; from the perspective of the interaction of field quantum, the acting force may not be equal to counter-acting force under the interaction of indirect contact; the gravity process is an exothermic process; in the gravitational process, annihilation effects may exist amongst gravitons; reciprocal translation may exist amongst fundamental forces.

@George, Allen, Pingan: thanks for your answers. Best wishes

@George: with regards to my paper on Primordial Rotation, at the time i thought it would be interesting if we can consider dark energy as phenomenon triggered by primordial rotation, but now i think it is perhaps caused by sound wave. A sound wave model of dark energy has been proposed by Dr. Xin-an Zhang. His paper is also available at http://www.prespacetime.com. 

Victor,

Let me do some reading.  I had not heard of this before but it interests me.  I am not sure of the rotation first or of the no rotation to start but I am convinced that regardless of the start rotation the reason that we seem to see everything rotating now is that the laws of physics and statistics are in the favor of rotation.

I think that the beginning of the Universe is in line with Karl  Schwarzschild's solution to  Einstein's field equations applied to  the existence of a particle. With further development of the theory of the  "black hole".,It is possible to prove that the smaller the mass of the black hole, the faster the acceleration of a forced, quantized absorption flow of zero point energy towards the inner singularity of the particle..  The acceleration of the flow is the the acceleration of gravitation, and possibly also carrying the strong nuclear force..Another equation gives the condition for the absorption, which becomes larger with the larger mass. These equations solved together, gives the mass of  a fundamental particle, with its absorbing capacity. This may have been the conditions for a random one particle creation, which created an avalanche of  particles etc. to become the present Universe. 

I think that nature has ways to avoid singularities. E.g. the two flows of air above and below an air foil, the section of a wing in an aircraft, have different speeds at the end tip: faster above than below: then viscosity enters into the picture and vortices appear to remove the "mathematical" discontinuity. Same happens when we have a supersonic flow that has to stop due to the presence of a solid object: then a shock wave is produced and the flow behind the shock is subsonic and no discontinuity appears. In the case of the initial stages of the universe, dealing with a theory with continuous variables like general relativity, we arrive at a "mathematical" singularity. Then quantum mechanics enters into the picture ad no singularity is in the picture. I believe that in nature there are no zeros nor infinities, no singularities. Nature is already "defined", and we have to understand it. Nature does not necesarily has to  follow our mental constructions.

Antonio, I agree, there are no singularities in Nature. But this makes singularities in our theories very interesting - these are the regions where our theories are false.  

Ilja: yes, singularities are very interesting. They are regions where the applied theory is not valid. In the case of the initial stages of the universe I think that GR just does not apply, it is a theory with continuous variables. Quantum mechanics may be the valid theory to apply. However, to quantize gravitation as it sounds may be is not the good way to go. May be to find a theory that quantize the space-time, as such, could give new light to the problem....

Antonio,

Your line of thinking is good.  I think that without black holes the model of the universe that we say (not me) is true the big bang is not possible.  I embrace that thought.

My one exception to this avoidance of the extremes is I think that infinity in the size of the universe is possible or at least an unbounded state with no end.

To the negative responses to a "singularity" I would like to go into the definition of a singularity. We have them all around us in different forms. For example, every step in quantum physics can be given as a singularity. The same with the processing of every bit in digital electronic processes. In the case of Schwarzschild's "singularities"  I am following a sequence of steps in a field of gravitation, which can be recognized as a "falling" flow ending in a black hole inside a particle. Because of the linearity of the relation between gravitation and mass, it is easy to break down the gravitation in a larger mass to a fine structure of particles. In the falling process, the angularity between the falling flow of  energy and the static distances to non-falling objects goes from a small angle at far away towards 90 degrees at the speed of light at the absorption of the flow in the particle. At this state, the flow is captured in the particle, without the possibility to escape. Call this a singularity or not is a matter of  semantics. 

Can the initial singularity be removed from cosmology models?

The answer is a question: Can cosmos be created without a singularity? There is always a step between existing and non-existing. Is that not a singularity?

Henrik: Imagine a sine wave in a cartesian reference system. Call the positive part of the wave EXISTING (something) and the negative part non-existing. NO SINGULARUTY IS PRESENT.

@Henrik, Antonio, Ilja, George: thank you for your answers. Yes it seems singularity can be removed in some cases. Best wishes

Henik,

I think that the definition of a singularity my be the issue.  I see your points about the singularity and change.  Also I like the way you think.  It is not just the standard line of thinking that has put us in the place we are today.  We must look at what we mean by, black hole, singularity, gravity, mass, energy, and space in order to understand that is really going on in the universe.

I also think that we are missing a step in the process of understanding by not finding a balance on a much smaller scale than the universe.  We must see the balance in the galaxy as one that we are ignoring.  This plays into the equivalence principle that I think we are missing between Entropy and Gravity.  There are equivalent  at specific points and this leads to the overall look of the universe. 

I agree with many here that if our theories predict singularities in nature, we need to keep scratching our heads.

There are so many ways out but which route should we pick? Extra dimensions? Time-varying constants? Exotic negative pressure fluids? Quantum gravity? Or, should we just give up physics until others have sorted out the problems?

I think a recent paper by Poplawski offers a very appealing resolution to the original question. It involves dropping what may well be an overly simplistic assumption built into general relativity by allowing for torsion effects that give rise to repulsion forces at high matter densities:

http://arxiv.org/abs/1111.4595

The theory is compatible with all experimental tests of general relativity but is difficult to verify experimentally (though less so than string theory perhaps).

Unfortunately, all proposals so far suffer suffer from the problem that they lack supporting evidence. Care to consider one that does not? The presence of complex life in the universe demands that the laws of physics be fine-tuned. However, a mountain of evidence already exists that the laws of physics are excessively fine-tuned to be explicable by the mere fact that humans have evolved on this planet. This evidence argues that the fine-tuning is not accidental. So I ask this: how can this excessive fine-tuning possible be reconciled with a universe that originated from a singularity? If we need reassurance that singularities cannot arise in nature, it is right here... waiting for people to stop ignoring it. To my mind, it is not a question of whether we can remove the cosmological singularity but a question of why so many still seriously entertain the notion that it even existed?

Robin,

I agree that we do not have to have a singularity in the beginning or any where else.   The point is that a singularity is a mathematical concept and only supported by math.

In reality we can not shrink things ever smaller.  There is a limit to how small something gets.  I am not however a big fan of the big bounce either.  Although I think that is a much better solution to the issue can can not fully embrace this concept.  It would be more likely if we saw it happen in the other galaxies or if we saw it on a galactic scale.

I really like your argument about life.  This is to complex to be chance with the given facts.  However this leads us into other realms that some may consider not scientific.

My thought has always been that there is a higher order in the universe that can be proved scientifically.  This requires a thought experiment.

If we take just two things in science and we play with them alone we can prove this.

1) Mass exists

2) Gravity works

We can put together a system that by the laws of physics look and act like what we know our galaxy to look and act like.  No matter if we use black holes or not.  In this case it may lead to the black hole but it can just as easily be removed.

Take mass and place it any distance make it any shape or size you like and do a random scattering of the mass.  It does not matter if you make the mass large clumps or the smallest bit of matter at the Planck length. 

Even if the starting point is so perfect that the sizes and masses are uniformly spaces and nothing is more massive than the thing next to it.  Something happens.  Quantum fluctuations happen and this means that two of the parts are moved out of equilibrium and they fall together.  As they break the equilibrium this forces the equilibrium every where to be off.  All across the vastness of space there is a chain reaction going off that cascades into particles falling together.  Think of the starting point as a solution that is super saturated.  It stays that way until something acts to disturb the balance. (Quantum Fluctuations)

As two particles fall together that are random the chance that they fall together with such accuracy that they have absolutely no rotation is  1/ infinite of chooses.  This in affect is a zero % chance that they are not rotating.  If we look into the night sky we see this to be the case as all things have a rotational quality.

By gravity the two particles that are rotating and have more mass than the outside particles will attract things at a higher rate as the mass is greater and will have motion that is angular in nature.  It will wobble in space as it is not perfect in shape.

This mass will continue to feed on the smaller masses that are closer to it.  The bigger the mass the more we see rotation and some remarkable things seem to be happening.  We can see that there is an axis of symmetry, and equator that as the rotation increases it bulges out ward.  This spinning ball when enough of the correct types of mass that are present in the universe accumulate or are created by the crushing forces of the large mass it will develop a field with an ability to move charged particles around the system.

This when you pull back and look is an electric motor or what we would call an electric motor.  I want to take it further than this and have but the point of this is that from total chaos or randomness comes total ordered systems.  This is a scientific fact not fiction.  There is a higher order to the universe and as scientists we should not ignore this.

We live in a very narrow band between total chaos and total ordered systems.

This model can be taken to the next step which is the mass gets big enough to collapse under its out mass and become a black hole.  Its equator would reach out much further as it fell in to the center and the rotation would be great.  This is sort of what the center of all the spiral galaxies look like.

There does not have to be a singularity at the beginning.

George, if the universe is to host life then an initial state of disequilibrium is essential. Fortunately, the universe is known to have begun in a state of extremely low entropy. Penrose has famously pointed out that inflation does not solve this 'problem' but greatly exacerbates it.

It's entirely possible that the angular momentum of the universe is non-zero, which might indeed have some consequences. Large stars have short lifetimes and so, when they die, they will typically retain sufficient angular momentum from the time of their formation that during core collapse the mass-shedding limit will be reached, heralding a change of topology in the core. A dense toroidal arrangement of electron or neutron degenerate matter can give rise to some interesting physics - capable of driving hypernova explosions and scattering elements useful to life deep into space. Incidentally, it's rather odd that we have several supernova mechanisms in nature capable of producing the raw materials necessary for habitable planets and doing so with virtually no waste. If the anthropic principle were correct, we ought to expect only a single SN mechanism, and for it to have a dismal chemical efficiency (for instance 0.01% metals with H and He making up the remainder). This is just one example of the weighty scientific evidence that life may in some sense be a goal of the universe (whether or not some people on this planet might be averse to considering this possibility).

Angular momentum could have macroscopic effects during the contraction phase prior to a big bounce. Perhaps entropy-resetting processes might then come into play, allowing an arbitrarily long series of life-hosting universes without any need for adjustments in the physical constants. The rotating black holes of general relativity contain ring singularities which are timelike and hence avoidable. They also possess closed timelike curves. I suspect the corrections to general relativity due to torsion as proposed by Polchinski might not change the situation all that radically until the bounce itself. I wonder if time travel within an imploding cosmological black hole might circumvent the second law of thermodynamics and open the door to entropy reduction.

As it happens, some of your points about angular momentum, gravity and electromagnetism chime with a model I proposed for quasars some years ago. Electromagnetism is far stronger than gravity and these are the only two long-range forces. But it is difficult for much electrical charge to accumulate on a spheroidal object as it will be rapidly neutralised. This difficulty, however, does not apply to toroidal objects. A spinning electrically charged torus gives rise to a magnetic field that can provide a highly effective defence against neutralisation by a surrounding plasma while also allowing long-range coupling between its rotational energy and charged particles that can result in collimated outflows aligned with the rotation axis.

The Universe must have had a beginning. Call it a singularity if you want. Mathematically, with different models, we try retroactively to calculate the age of the Universe. I think that the date of the start of our Universe was randomly depending of an initial code of mass and energy to be available within a small enough volume for the quantum physics to  start up the job.

Henrik, a number of cyclical cosmological models have been proposed over the years. Do you have any evidence that they are all incorrect and how does quantum physics result in such extreme fine-tuning of the physical constants?

Henrik: The Hawking "bubble" universe is an example of a self-contained surface that doesn't have a singularity (other than a coordinate singularity) at the Big Bang location –  worldlines extrapolated back through 0,0 simply curve back into another region of space with their time-polarity reversing as they pass through 0,0.

To an inhabitant of a Hawking "bubble", their universe could appear to be cyclical and the result of a perfect mirror-image of their own universe contracting to 0,0 to produce a start-point for the Big Bang, and then reemerging as their own universe, with both universe-surfaces touching at 0,0. So although from the outside we could see that there was no such thing as "before 0,0" in that universe,  from the inside, the apparent mirroring that happens at 0,0 creates the appearance of a previous universe to explain the inhabitants' questions about "what happened before 0,0".

I'm not saying that our universe necessarily //is// a Hawking bubble, but the "bubble" geometry is one apparently logically consistent scenario in which there's no such thing as "before the big bang", without that universe's internal logic breaking down.

I think the anthropic principle may play a roll here.  We apparently live in the universe that we do because if the universe were any different from the way it is we would not be here.  

Doesn't look like disciplined research...so, a comment or two:

1. A GR black hole as viewed by Newton on the outside needn't 'show' a singularity...

2. If an event horizon on the outside evaporates there's probably more vapor inside...

Ray.

@Robin, George, Eric, Henrik, Raymond: thank you for your answers. I am curious that quantum mechanics can provide a way to avoid singularity. Does it also apply to classical physics, provided we can model the universe using the classical wave/Helmholtz equation? What is your opinion? Thanks

Victor,

If we are to take the Quantum Mechanics approach seriously there is no way to define a "true black hole" as there is no way to have a place where there are no fluctuations.  

I think this goes back to a problem that we have had before with definitions. 

@George: thank you for your answer. 

@all contributors: i just found an interesting paper on singularity free wave scaterring problem, see http://arxiv.org/pdf/1002.3993.pdf. Do you think that this paper may shed a light on singularity problem of the early universe? Best wishes

Victor, someone might claim that the Earth began as a tiny speck in space that spontaneously expanded to its current size through exotic physical processes that forever lie beyond experimental reach. Although I very much doubt that anyone here would be impressed, how is the traditional view of a singular big bang superior to this? I'm not disputing that there was some kind of big bang or that the cosmic microwave background can tell us a great deal about the early universe, but there is a big difference between observing the universe as it was 1013 seconds after the big bang and extrapolating back to t=10-∞.

Consider the gravitational potential of a singularity. It literally has the potential to create nothing, let alone craft a finely-tuned universe. On energy conservation grounds alone, the notion of a primordial singularity does not bear scrutiny. To my view, the introduction of ad hoc physics in order to preserve some rather bizarre, simplistic view of cosmogenesis is inappropriate. In answer to the original question of how can the singularity be removed, what is wrong with good old-fashioned conservation laws? Have they not withstood every experimental check we have subjected them to?

By the way, observation, even combined with general relativity, does not lead to the conclusion that there has to be a big bang. 

The GR theorem that there has to be a singularity depends on assumptions about matter which are known to be wrong.  For usual matter, the expansion rate would be decreasing, a''(tau)0.  We have strong observational evidence for this, namely the size of the inhomogenities of the background radiation.  These inhomogenities should have a common cause -  a common event in their past light cone, which is not the singularity itself (which, as a single point, could be at best the cause for homogenity).  But there are no such common events in the past light cones of different parts of the same inhomogenity, if a''(tau)0 in the very early universe. 

But once there is such an unknown thing which makes a''(tau)>0, then it can also prevent the singularity.  There can be a non-zero starting point a_min, so that a(tau) sim a_min + b exp(tau), but transformation of the big bang into a big bounce, with a(tau) sim a_min + b tau², seems even mor plausible.  

Last but not least, there is something which makes a''(tau) positive once a becomes very small. The natural expectation is that this unknown cause makes a''(tau) even greater than a(tau) is smaller.  To "save" the singularity we would, instead, have to assume that this unknown effect leads to a maximal a''(tau) near some a_critical and then, for a

Robin,

I agree with you.  The initial singularity is and has to be false.

George,

I think the argument can be strengthened by considering black holes. I find the notion that they contain singularities also impossible to take seriously. In fact, I would go so far as to say that gravitational time dilation prohibits the formation of genuine event horizons. In Oppenheimer-Snyder collapse the event horizon forms only in an asymptotic sense as the proper time along any timelike curve either external to or on the surface of the collapsing star approaches infinity.

What about the interior perspective? Won't these particles become trapped within an event horizon in finite proper time? It may seem that the answer to this is yes, and indeed many people believe that to be the case. However, I think this is a grave error. Even though in principle there is freedom to select different frames of reference constraints inevitably apply to the spatial or temporal range of a chosen reference frame due to the existence of possible alternatives.

If we regard the spacetime of the universe as a monolithic four dimensional continuum then because the universe is finite we have the rather obvious constraints that any measure of length must be finite and any measure of time must be finite. Seems rather trivial but the consequences are not.

Let's say that a test particle within a collapsing star would in theory find itself trapped within an event horizon after a proper time of one hour and that it would "reach the singularity" one second later. The problem now is that we know the proper times of particles outside the star reach infinity before the test particle's hour is up. The naive expectation that time can continue for the test particle beyond this is wrong since it would necessarily violate the global integrity of the spacetime continuum. Another way of saying this is that when the time dilation between two clocks becomes infinite, one of the clocks must cease to advance. Failure to respect this may not seem to incur problems locally but it implies unphysical situations elsewhere.

It seems the universe will be here for quite some time so we can safely say that gravitational collapse has not quite produced black holes with event horizons yet. Rather, these objects are essentially frozen in time. For one thing, we can immediately dispense with the idea of some paradox involving loss of information in black holes. If no event horizons have yet formed then no matter could have crossed them and hence black hole singularities do not exist. This also tells us that astrophysical black holes do not conform to any of the stationary/eternal black hole metrics (although in many cases the Kerr-Newman metric may well approximate the exterior geometries of realistic black holes).

The impression I get is that a black hole is what forms when a gravitationally bound system runs dangerously low on energy. Graviational time dilation freezes all motions (including those of photons) preventing an event horizon from forming. The total energy remains marginally above zero, consistent with the minuscule scale of the Hawking temperature. A possible inference is that nature abhors negative energy states. If so, a point of infinite mass density could never form and so the universe could not have begun with a singularity.

Robin,

I think the only way that black hole could exist is if the Schwarzchild calculations are wrong and things collapse at lower densities creating a larger mass that is not quit as dense.  It is one of the reasons that singularities are so untenable to me.

I was hesitant to talk about the rest of the model as it goes against some of the principles that we take to be true but have no real proof for.

The speed of light is just the number or velocity at which a photon propagates relative to mass.   It putts into question the light postulate and its interpretation.  It also allows the blending of QM and the relativistic model.

The rest of the model deals with the event horizon issue and the collapse where the force of the rotation and the event horizon will interact and create an accretion disc around the body.  This is disc is outside the event horizon and creates the disc shaped galactic bodies that we mostly see in the sky.  

The biggest problem is getting over the speed of light being a problem.  In relativistic Physics we are stuck between a rock and a hard place when it comes to this issue.  Most will tell you that space bends and warps but the limit is not broken how ever they realize that some things like Cherenkov radiation can not be explained by the bending of space as the issue is in a mass.  I hope that you get my point we are hopelessly deadlocked in the past when it comes to our view of light.

You are very right about the finite look at things in the universe and the idea behind that.

I think as far as the time clocks go the problem stems from our misunderstanding of the "Ability to Measure time"  Any force put on a body creates a "drag"  This is thought of as the gravitational potential but in reality it is the only because of the Pauli Exclusion Principle that gravity and its affect do not make everything into a black hole with the force of gravity pulling things to higher and higher densities.  If it were not so then everything inside would be so close to the next thing that there is no way to have the ability to measure time as it is measured by movement of things.  Things in a black hole cannot move that way and therefore there is no way to measure time and hence time stands still.

Again this is a different way to look at the problem.  I will need to write the book on this.

Cosmology without prejudice does not have the singularity.

http://www.stfi.ru/journal/STFI_2014_04/nurgaliev.pdf

I agree.

Dear George,

can you see the cosmological model without prejudice and without the singularity on this pdf file?

http://www.stfi.ru/journal/STFI_2014_04/nurgaliev.pdf

@Robin, Ilja, George: thank you for your comments.

@Ildus: I have read your paper, it is very interesting indeed. I see that you use Raychaudhury equation, but how can you prove that it exhibits voriticity in early universe? I think one possible way is to find link between Raychaudhury equation and Navier-Stokes equations. see the enclosed paper by Zalaletdinov, in particular read section 10 and theorem 7. What do you think? Your comments are welcome. Thanks (see also my private message to you)

The  Raychaudhury equation exhibits vorticity not necessarily in the earliest Universe only, but at the all stages of the Universes evolution.  It becomes strongest repulsive factor "winning" gravitation at the the earliest dense stages providing displacement of contraction by expansion and accelerating the expansion. "Dark energy" is energy of the vortexial component of the cosmological flow. Thanks for the reference to the Zalaletdinovs paper!

Dear Ildus, thanl you for your comments. Allow me to send you my new paper citing your work too. I welcome further discussion or possible join writing. Thanks

A reference to the following (enclosed) earlier publication too just before [7] would be an appropriate one (you might find interesting  its last conclusive sentences).    

Dear Ildus: thank you for your paper, yes I have read it, but i think your STFI paper is the most convincing. Btw, it is just pedagogical paper. If you wish, we can do a second paper where we explain in detail a cosmological model based on link between Navier-Stokes and Raychaudhury equation, then we can extend it to Cantor Sets. But if you are busy, it is fine. Thanks

CUTE: If we compute the mass-energy at the center of a collapsing cosmos we find its gravitational contribution to the in-falling kinetics is draining its mass-energy, A. hollowing it out as in the Thread Question, or B. 'til it's a deBroglie-mass-wavelengthening explosively, big, bang...

Thank you Raymond, do you have a paper in this direction? Thanks

No nor preprint yet. It is part of a much larger question that I've been working on—no definitive answer yet: The question goes like this: Where is, potential energy (e.g. a gravitational system): If it is in the field exactly where the test-particle is, then there is constant energy available at each radius and therefor integrates to infinite over all radii to infinity: I expect-rather it's a power-limited draw-in at the speed of light, (which lead to the previous 'cute' item), and all-in-the-research-works presently, with all the 'otherwise's.... It's one of 200+ 'questions' on my Cosmology Structures course final presentation (a bit longer than it was supposed to be)...

P.S. I post powerpoint-video-trailers on my research, to youtube.

P.S. #2. On the theological aspects of your paper-reference, I do have a correct, thorough revision (online) to the Genesis chronology, based on Biblical, Egyptian, Sumerian, extrabiblical and followon documentations: right down to photographic proof (NASA imagery) of humans, dinosaurs, religious artifacts... on Mars, (Don't laugh 'til you see the pupil of the eye of the dinosaur: its species-name rhymes with 'cry-or-laugh-o-saurus')...

Dear Victor, did you get publicized yours? Is it available?

Dear Ildus, yes my paper has been published in August, 2015, at http://prespacetime.com/index.php/pst/article/view/791.

Enclosed i send you another paper that I wrote in December but lost in my PC, and just recovered. It discussed electrodynamics of superconductor. Your comments are welcome. Thanks

Dear Victor, probably, your enclosing not another but the same article could be more convenient for you. Otherwise, my 5-dollar payment as a PayPal fee can embarrass you for the reading "The route is by showing that Raychaudhury equation leads to Friedmann equation when the vorticity vector, shear tensor and tidal force tensor vanish." . What you think? 

Dear Ildus< sorry my previous link was not meant that you should buy it, because i already uploaded30 days ago. But here allow me to include the revised version again.

What I meant with the statement is that Friedmann equation is important for cosmology model, that is why to me it is important to show that Raychaudhury equation reduces to Friedmann. The next step is to show how one obtains Raychaudhury equation from Navier-Stokes equations, If you know that, please kindly send your paper. Thanks

Dear Ildus,

How do you do? Hopefully you are in good condition. Btw i just completed a new book discussing TOE. The title is : A Biblical Theory of Everything inspired by the Johannine Prologue. If you wish, I can send this book for your preview. Please let me know your email. Yours,

The PFO-CFO Theory contains no singularity (see my and Elena Kadyshevich ResearchGate pages). 

Dear Victor Christianto,

Yes, of course. See my or Elena Kadyshevich publications about the PFO-CFO Theory in our pages of the ResearchGate site.