1. OS thought, and this was accepted by the BH’s supporters, that the picture in terms of the world time t is not complete, but in terms of the proper time is complete, since the latter covers that part of the particle’s evolution that goes “after” t=infinity and therefore “is not visible” to the external obs.

The paper shows that the description in terms of t is complete, since “the worldlines of the star’s particles in the exact solutions of the Einstein equations obtained by the OS method cover every moment of the existence of these particles in the real world and therefore these solutions give a complete picture of the evolution of the star. The irreversible dilation of the proper times due to relativistic and gravitational time dilations is the objective physical phenomenon that stops all processes in the star, including the process of collapse itself. This specific and fundamental physical phenomenon basically distinguishes the collapse scenario of the Einstein gravity from the Newtonian one, where there is no such stopping mechanism. “(from the Conclusion)

2. The OS has found a particular internal solution (i.e., y(t,r), metric and world lines) only for the parabolic velocity (velocity=0 at r=infinity). I was able to find a complete exact solution (including y(t,r)) for all velocities that preserve the homogeneity of the density, i.e. including elliptic (velocity=0 at r=R) and hyperbolic (the velocity is finite at r=infinity).

3. In addition to the solution, a physical interpretation is also needed, which includes a physical picture of the process (including visualization), a clear separation of the physical and non-physical regions of variables, finding expressions for asymptotes for the inner layers, the moments of freezing of the proper times. All this is done for the first time for all three velocity regimes.

4. It is shown that the BH picture refers to the non-physical region of the variables (t>infinity) and is therefore forbidden by general relativity, since in stars embedded in the real universe all worldlines of particles remain timelike during of real cosmological time (t<infinity) (for non-zero mass particles) and the singularity at the center and the event horizon are never formed.

]]>I am glad that freezing is strictly proved and let all those who believe that they see the collapse into the horizon, or show on the world lines of the exact solution where and when this happens or will be silent.

]]>This condition is also important in that it allows us to introduce a hypersurface of simultaneity with the world time t inside the star too (the clocks can be synchronized uniquely only for a diagonal metric).

By introducing the auxiliary function y(t,r) and finding it from the diagonality condition, the OCs were able to find exact solutions for both the metric and the particle trajectories inside the dust star in the Schwarzschild coordinates r,t. In the OS article only the final result is given for y(t,r), but I was able to restore their derivation in details and presented it in the Appendix.

In the literature (in textbooks too), a misleading tradition has settled, that as the OS solution, the same general Tolman solution in the comoving coordinates, but for a homogeneous star is given.

If this were the case, then it would only be renaming the homogeneous Friedman solution, well known even before Tolman, to the OS solution, which is strange in the first place, and secondly it is humiliating for the OS reputation, since it would simply be plagiarism.

But what about in reality?

In fact, for such an extended object as a star, an exact solution must be given on the hypersurface of simultaneity, so that

a) the positions of all particles were given simultaneously and

b) on the surface the solution was smoothly matched with the external Schwarzschild solution.

OS is well understood that and the internal Friedman-Tolman solution transformed into the Schwarzschild coordinates, which allowed them to carefully sew it with an external static solution.

But for an explicit solution, one must introduce and calculate the function y(t,r) from the diagonality condition, which is the highlight of the OS method. Without this function, there is no exact solution in these coordinates, and hence it is impossible to determine the structure of the star as a whole.

Thus, the OS solution represents the Friedmann-Tolman solution, transformed from the comoving coordinates into the Schwarzschild coordinates for the diagonal internal metric and the matching with the external static solution by means of the function y(t,r) following from all that.

]]>The value of this work, in my opinion, is that the problem of collapse – freezing is solved analytically.

At the time of Oppenheimer and Tolman, they tried to solve it analytically, but with the advent of the computer, analysts were completely superseded by the numerals.

They declared an ideology that asserted that all problems that could be solved analytically had long been resolved and the future of physics is numericals. This ideology was necessary only to them, since justified the priority in physics to those who can solve problems by numerical simulations only.

They most likely conceal the fact that 100 times the calculation gives 100 contradictory results, they choose the one that they think is the most believable and pretend that their results should always be believed.

The analytical result obtained in this article is a worthy answer to all of them. If they now compare their results with this, they will know which one of them happened to be right accidentally.

]]>This is an ordinary phenomenon at paradigm shifting periods (see Kuhn’s book).

Notice, my reply to you in the LinkedIn blog has been removed by moderator. So, if you interested by real science, describing real world, and can read the research papers, not only their abstracts, below I present my reply without censorship:

“@Peter: “as I learned GR, the proper time continues on at it’s “proper rate” as objects fall towards the event horizon of a black hole. The distant observer sees the motion of the object slow down, slower and slower as the event horizon is approached – so that in the limit the object appears frozen at the event horizon.

But in the objects reference frame it is actually accelerating, and will zoom right through the event horizon. ”

Peter, as you “learned” is not GR, but BH paradigm, which is illegal hybrid of GR by Newtonian BHs and contains obvious internal contradictions. Main of them is following:

As you know, in GR the worldline r(t) of a particle on a falling dust shell, parametrized across world time t, does not cross grav.radius 2M eternally r(t)>2M, while exists our Universe – this simply follows from the Schw. solution, an exact solution of Einstein eq.

You also must know, that in GR the worldline, not only its small intervals, is invariant, and set of events along it does not change at any parametrization, thus at turning to proper times tau(t), as another parametrization of the same set of events, you again will come to the same restriction: r(t)=r[tau(t)]>2M.

A mistake in BH paradigm is ignoring of this constraint for any proper time moment be related by a definite moment of real world’s time t< infinity.

See also last discussion about frozars vs BHs, where I explained why GR leads only to frozars, while G.'t Hooft attempted to defend BHs:

@Peter: "you are the editor of the journal which published your paper".

We live in the period of deepest crisis in fund. sci. One of consequences of that is breaking of scientific ethics by editors of leading journals, who reject papers contradicting to "mainstream" paradigm directly or send them for peer reviewing to experts having conflict of interests.

In this situation I follow to one of best traditions of world economy – to guarantee quality of produced good by own name as a trade mark – my papers do not contain arbitrary hypotheses, internal contradictions and are based on experimentally well checked theoretical principles only. If they contradict to commonly accepted and "learned" concepts, mistaken are latter and they should be improved without hysterics.

In the case of collapse, we follow GR in the frozar picture, which described in my papers (independently where they are published!), and break GR in case of BHs.

]]>Still lack of response of professionals I understand as “Silence gives consent”. ]]>

http://www.linkedin.com/groupAnswers?viewQuestionAndAnswers=&discussionID=175477793&gid=3091009&commentID=100079472&trk=view_disc&ut=1hUeCZBThExRs1 ]]>