Supplement1

One more kind of questions concerned Hawking’s variation of black hole conception. To clear the situation, we have to understand that Hawking’s conception is secondary in relation to the general black hole conception and does not touch main problematic aspects of their formation. For example, in studying the gravity collapse as the basis of his further work, he proceeds from the premise that for an uncharged non-rotating black hole, “its final stationary state is described by Schwarzschild’s solution with the metric (4)” [28, p. 486]. He is right noticing, “the seeming singularity at r = 2M is fictitious and is simply caused by an unfortunate choice of coordinates” [28, p. 486]. At the same time, he transfers the consideration into description of Penrose diagram in which “inside the object the metric is basically other, the event horizon of the past, the singularity r = 0 (corresponding to Schwarzschild’s R - Authors) in the past and second asymptotic plane region do not exist and are substituted by a time-like curve which visualises the origin of spherical coordinate system” [28, p. 487]. But with it the region 0 < r < = 2M (which in Hawking’s symbols corresponds to 0 < R < = 2M), i.e., from the view of measured parameters, the region of negative measured radii r determined by (3) has been retained. This allowed, on one hand, to implicitly admit the BH conception absurd, and on the other hand, manipulating with the symbols R and r (of which we just said above), to virtually retain the event horizon and the features at this horizon. In accordance with Fig. 3 of the cited paper [28, p. 489], in the origin of coordinates corresponding to the negative value of measured radius-vector (in Schwarzschild’s symbols r = - = - 2M), Hawking represents the non-singular centre of the body, which is also absurd from the view of physics. We wonder, how he either his followers would go negative way to the past.

As we see, both Penrose and Hawking clearly realised that Schwarzschild’s solution contains a mistake and well understood that in reality in Schwarzschild’s solution the singularity is seen only in the centre and is caused by the statement of problem. At the same time, having a wish to retain the convenience of conception of all-consuming black holes, which was formulated on the basis of incorrect solutions, Hawking introduces a negative radius in spherical coordinate system and negative time. And even with these mythical parameters he is unable to put his fantasies in agreement with reality. Thus, factually Hawking’s conception is rather a corroboration that he understood the full inner inconsistency of the basic relativistic conception. And with it the efforts are addressed not to improve and to put in agreement the underpinning of the basic conception. The efforts are reduced to small retouching of corollaries - in particular, a direct corollary that so massive celestial body, having achieved some value of mass, would be unable to stop sucking in new and new substance, up to having sucked the entire universe. While Hawking writes, “due to the quantum-mechanical effects, black holes can give birth and emit particles, as if these would be bodies heated up to the temperature

where ₁ is the frequency of radiation and ₂ is the frequency of light registered by the observer in a weak gravity field, when observing from the weak field region, the frequency of this light would be practically zero. And this process has nothing in common with the effect of tunnelling through the potential barrier in quantum mechanics. In this last case the frequency of wave packet of an electron will not grow in approaching to the barrier. And since in accordance with BH conception the whole substance of black hole is located lower than the event horizon and the event horizon is factually the surface of black hole, a BH basically cannot radiate infrared rays, and with some finite thermal temperature. Furthermore, according to the conditions of black hole formation, there is no grounds for temperature growth near the black hole, as such growth accompanies the molecular interaction, which would inevitably counteract the unlimited compression of substance, - and we pointed it in our paper. Because in accordance with the black hole conception, when the substance falls onto the centre of celestial body, it does not encounter any resistance, does not increase the pressure, does not rise its temperature due to the interaction inside the super-compressed substance. And it is impossible to clear these conditions in limits of black hole conception, because it was built exceptionally with the account of gravity field by way of geometrisation of interaction in this field.

We would like to add, striving to implement his virtual ideas in some physically associative appearance, Hawking, in particular, presented the birth and decay of particles in the form that clearly contradicts both basic postulates of mathematical formalism and physical associativeness of processes. “I am using in this paper the approximation in which material fields, such as scalar, electromagnetic or neutrino field obey usual wave equations, if in them we substitute Minkowski metric by the classical space-time metric g_ab. This last satisfies Einstein’s equations with the source in the right part equal to the average value of properly determined operator of energy-pulse of material fields. With such formulation of quantum mechanics in the warped space-time, there arises the problem of interpretation of field operators as operators of annihilation and birth. In the plane space-time, potentials usually are decomposed into the positive- and negative-frequency components” [28, p. 480]. Well, after Hawking we would be able to see these negative-frequency spectra corresponding to the operator of annihilation, in space or at least in laboratory.

One more circle of questions showed the colleagues’ attempt to attribute the origin of black hole conception not to Einstein and his followers but to the giants of classical physics, specifically to Newton and Laplace. With it, the colleagues directly or indirectly relied on the fact that both in Newton’s gravity law and in the potential theory, there exists the singularity in the centre of field, and it is caused by the inverse quadratic regularity of the gravity force against the distance. Yes, of course, this problem existed, and existed even a deeper problem of the universe stability with mutual attraction of all its parts to each other. In particular, Newton wrote about it in his letter to Bentley of December, 10, 1692 so: “It seems to me that should the matter of Sun and planets and generally the entire matter of the Universe be uniformly distributed in the sky, and should each particle have an innate gravity to all others, and should the whole space in which the matter has been distributed be finite, then the matter from the ‘outskirts’ of this space, due to gravity, would tend to the matter in the centre and would fall there, due to which it would produce one tremendous mass” [5, p. 126]. However, this does not mean that the initial difficulties that existed in classical physics are still so acute and have no way out except to submit itself to the inevitability, the universe to be shrunk into a point, and to admit the central singularity of gravity field. Not in vain we in our paper, page 9, began our estimation calculation of pressure in a gravitating body with the long-ago-known regularity (formula (48) of the paper), which showed that in a gravitating body of finite diameter, the attraction of parts of a body falls with a decreasing radius. With it, not a singularity but the absence of gravity takes place in the centre of body. While the singularity that is present in Newton’s law and takes place in Laplace’s solution for the potential theory is not a mistake of classical conception but the consequence of approximate modelling, which neglects the size of gravitating body in comparison with between-the-bodies distance. But this approximation restricts also the limits of this model’s applicability to some considerable distances between the bodies. At short distances and especially within the body, as for example in modelling of processes in a dust sphere, we have to account that the gravity force affecting the body is proportional not to the whole volume of the body but only to that part which is located on smaller radii. And it was already Newton who understood it well: “Gravity to the Sun consists of gravity to its separate parts and with the distance from the Sun it decreases in the exact proportion to the squared distances even to the Saturn orbit, which follows from the rest of aphelia of planets, and even up to the extreme aphelia of comets, provided these aphelia were at rest” [6, p. 662]. This feature of gravitation interaction applied to the conditions within the body causes the descendent regularity of the gravity force with the decreasing distance from the body’s centre. Thus, the regularity with a singularity in the centre, which relativists tried to replicate in the black hole conception and in GR, is basically inapplicable to model the phenomena inside the celestial bodies and in the region close to celestial bodies, nothing to say that the very relativistic approach is erroneous in its essence.

This feature makes the relativistic conception on one hand fully different from classical conception of gravitation interaction, as it substitutes the study of direct interaction of a body with the field by geometry of reaction of constraints in the virtual field. On the other hand, the presence of such virtual field, which is obviously non-elaborated in GR, makes this conception fully undetermined and disabled. We see it practically, as GR considers a very narrow class of possible motions of a body, out of this class of motions the calculated regularities are violated. While in classical formalism we can study any motions of a body in gravity field, at any angles and in any direction. The only limitation of classical conception is meanwhile the static type of the field. This limitation is surely temporal and will be overwhelmed. While the relativistic conception, also proceeding from the stationary gravity field, but based on the dogmatisation of existing regularities of classical conception and on variations of basic regularities without due substantiation of phenomenology, is basically unable to provide a physically correct passing to dynamic fields.

The second difficulty of gravity field connected with the stability of mutual position of celestial bodies also was gradually solved. In particular, a great step towards the solution was made by Eddington [7] and Frenkel [8, chapter 7]. In different versions they premised the possibility, electrons of atoms in the nuclei of stars to become collective under gravity compression. More completely this conception, noting the features of gravitational compression of a protostellar cloud described by Shklovsky [9] and essentially improved, has been developed and quite long time ago published by us [10]. This conception is well consistent with the known and newly obtained data of Sun system and distant celestial bodies, and the main, it fully lifts the problem of unlimited compression of the substance of universe. If noting that stars and stellar associations form electron cocoons, mutual gravitation attraction of hot celestial bodies is effectively compensated by mutual repel of electron shells of these bodies and this, on one hand, impedes the unlimited compression of the entire substance of the universe, and on the other hand, it prevents star collision and cannibalism of galaxies. In this way the difficulty which Newton saw in his conception has been lifted. And lifted not in frames of gravity conception but in complex modelling of star formation, i.e. in the way so typical for classical physics. It is important that although we made our study well later than GR and BH theories were created, the underpinning of model which we develop was built as long ago as at times when these conceptions were under way - and Einstein, Schwarzschild, Freedman, de Sitter either Kerr did not take it into account, despite the effects on which Eddington’s and Frenkel’s conceptions were based are obvious and physically grounded. Their reason was not that relativists did not understand the importance of, e.g., thermoemission processes, but that this could not be inscribed into the model of abstract geometrical substitution of physical fields. Moreover, even should GR creators dare to account such factors, which would make the metric dynamical in time, they would have to forget their hope to solve the modelling equations even in an approximate and limited appearance. But even without it, in Einstein’s form, their equations remain unsolved and hardly will be ever solved. This makes the relativistic way fully fruitless, nothing to say of their perverted way to account the dynamics of processes that brings the results absurdly discrepant from the view of physics.

Thus, it is incorrect to rely on some initial either idealised models of classical conception, disregarding the further developments and features of the modelled phenomenon. The more that in distinct from classical conception, the relativistic idea has fully emasculated the physical meaning of gravity interaction, having substituted some convenient for relativistic conception amount of physical properties by the geometrically warped space-time metric. With it, account of any properties or factors that have not been inscribed into that conception - such as decrease of attraction inside the gravitating body, or temperature growth with the compression of a body, or exponential growth of pressure with compression of substance - wipes the relativistic model out. And this is quite regular for conceptions built on some convenient amount of manifestations of physical phenomenon by way of dogmatisation of its laws.

Among the questions raised by colleagues in analysing our study, there was the following: when giving the regularities of pressure growth with the substance compression, and estimating the pressure inside the body caused by the gravity interaction of the parts of body with each other, we considered the static, not dynamic model. Here we first have to mark that in the sense of gravitating body formation, both GR and BH models are static. Otherwise they would have to account in metrics the transformation of spatial metric tensors in time, and Einstein in developing his GR would have to ground it not on Poisson conservation law but on the dynamic analogue of this law, which we yielded much later in the course of proving the related theorem [11]. Having it available, we had no necessity to consider the dynamic problem. Furthermore, the very fact of presence of substance counter-pressure which we showed, as well as limited growth of pressure to the centre of celestial body comparable in its mass with the calculated black holes, fully destroys the phenomenology of black hole modelling based on free fall of substance up to the centre of gravity field in the growing strength of gravity field. In our paper we showed it quite completely. And the calculation which we made was an estimation, as we said there. The complete calculation would have to account much more amount of factors caused by the growing density of substance with the growing pressure, and the influence of thermodynamical processes. This would make the calculation too complicated, the more that it is enough large work per se.

SELF	2
S.B. Karavashkin and O.N. Karavashkina