SELF |
10 |
S.B. Karavashkin and O.N. Karavashkina |
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5. Infinite gravity compression We showed relativistic constructions to be fully
abstracted from the physical meaning of processes; we can see a next bright example in the
problem of dying stars. The paper by Oppenheimer and Snyder [28] whose name we have put to
the title of this item is one of typical in this sense. In this paper the authors study "stars of large masses (> 0,7 M We from our side also will not analyse a clearly artificial and unfounded reasons listed by the authors, which could bring the change of initial mass of star. We will focus our attention on the methods to prove the ability of celestial bodies to collapse. Unfortunately, the methods are same. To begin, Oppenheimer without 'excessive' pondering introduces the Schwarzschild's metric, which is known to be describing the field of point gravitating mass - and, as we showed above, describing erroneously. But the main, this metric describes the field out of mass, and Oppenheimer showed his understanding of this shade when introduced the metric: "If in this case we may at the later stages of compression neglect the gravity action of any radiation either substance leaving the star, as well as the deviations from spherical symmetry caused by rotation, then out of the limits rb of distribution of stellar substance (italicised by us - Authors) the interval has to take the form |
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(53) |
where Naturally, such statement of problem does not satisfy the authors, even though they distorted the definition of Schwarzschild's radius. As we revealed before, this means the singularity of metric, not the radius of gravitating body, which in Schwarzschild's problem was infinitesimal. So Oppenheimer and Snyder immediately apply the relativistic method to 'adjust' the phenomenology. At the first stage the authors introduce: "As the pressure of stellar substance is insufficient to counteract the forces of own gravity attraction of star, it probably will begin compressing, so that the boundary rb will unavoidably diminish to the gravity radius r0 . The local observer located nearby the stellar surface, where the pressure anyway has to be low, will see that the substance goes to the depths with the speed very close to that of light. But a far observer will see this motion in (1- r0 / r)-1 times slower" [ibidem]. It is easy to understand from the cited statement of the problem that the authors have crudely violated both classical and relativistic idea of the phenomenology of real processes. This does not advance the authors to the result they want to achieve, as the conditions for which Schwarzschild's metric (53) has been written remain inviolable. For the relativists, this inconvenience means the only: they need to retain the metric, changing the conditions, - and the authors start it. "Let us think the substance inside
the star to be distributed in spherical symmetry. Then we may take the interval as
(53)" [ibidem]. As we see, this is very
simple. If no substance - the metric (53) is true. If the substance is present - too, if
it is distributed in spherical symmetry. No difference. With it the tensor of
energy-momentum In the view of Relativity, Oppenheimer and Snyder also are highly mistaken. For two observers, if one of them is near the body's surface and another is distanced from the surface, the speed of substance flow on the surface of collapsing body also will not seem to be so much different as the authors predict. As we revealed in the item 2, it follows from Einstein's views that for observers located at the inertial reference frame in gravitating field, the light velocity is constant, as namely this value Einstein puts to all his formulas. The fact that later he denies his statement of problem is already insufficient from the view of physics, as the formulas have been yielded namely under stipulation of constant speed of light in the view of inertial observer. Naturally, with so deep inconsistency in the reality and
the authors' wish to stipulate the collapse of the system, they could not put their
understanding in agreement even in frames of clearly unphysical representation of
Schwarzschild's metric. And they confessed: "We did not succeed
to integrate these equations (the field equations - Authors)
doing not putting the pressure equal to zero" [28, p. 355]. But this did not
stop a least Oppenheimer and Snyder in their striving to prove the collapse anyway. They
again and again modify the conditions of problem. In the end of ends, all versions were
reduced to those which appeared convenient to achieve the target, but are inconvenient by
virtue of conditions inconsistent with the collapsing star at which they consider the
current problem: "To answer this question, we will find the
solution of field equations for the limiting case of tensor of energy-momentum, when the
pressure is zero (! - Authors). In absence of pressure, the
field equations do not have statical solutions, except when all components of |
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(54) |
[ibidem, p. 356- 357]. Thus, it follows from the modified statement of problem that in the model of star, the pressure in the star has to be zero, tensor of energy-momentum also has to be zero (any processes are absent and the star has no energy), but the density has to be non-zero and in some way uniformly distributed in the star. The only question is, what concern this so-to-call model can have to real processes? Nothing to say of instabilities, redistribution of mass, mutual affection of substance in the star, of thermodynamical processes; but even in limits of relativistic geometrical approach? Of course, it is irrelevant. But namely these solutions separated from the stipulations under which they were derived have been elevated by relativists to the level of unquestionable, thoroughly substantiated, and even observed by some people somewhere. |
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