V.5 No 2 |
3 |
Supplement 2. The answers to Sergey Khartikovs questions | |
3. Citation: Sorry, in this item I see you confining
yourself to some Brief course
which you initially did not show. The
issue of linear element of metric is reduced in this case to the fact that in passing to
GR, Einstein had to retain the basis of SR in the local sense, i.e. in constancy of
gravity potential, and namely in this sense Einstein required, the elements of metric to
be linear, as in SR the metric of 4-D interval is linear. Sergey, in presence of gravitation, all solutions of GR have a non-linear metric. In Schwarzschilds work he did not state his metric linear (it only in the limit, at the infinity, tends to become linear). The words linear element which Schwarzschild uses mean in mathematical analysis only one thing: the differential of length of the arc ds. You saw the discrepancy that Schwarzschilds solution is nonlinear, while Schwarzschild said, linear element . Only in this meaning I objected: Schwarzschild did not state the metric linear and used this word so as it is done in mathematical analysis. Of Einsteins requirements I will tell below. Nothing new is that relativists write one, say second and
mean third. They say of the equivalence of inertial and gravity masses and mean the
equivalence of laws in IRF and NRF. They say of intrinsic RF and use it as an accompanying
one to study the non-inertial motions. They say of full identity of IRF in SR and separate
RFs into the accelerated and being at rest
they say and mean many things. |
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(20) |
No sense. This interval has no invariance. It does not
determine a real trajectory of a body. The Lorentz transformations are not true for (20).
It only comes to paradoxes of zero interval in a near-light-speed motion of
the body. But on the other hand, without the 4-D interval, GR is impossible. Einstein has
found the only chance - to retain this interval locally. For it, he needed, the metric
with which the interval was postulated in SR to be linear. So Einstein said of local
metric, and we showed it in the Supplement 1. While the nonlinear metric is senseless in
GR, as in GR only local operations in the metric are admissible. 4. Citation: You, dear Namesake, are neglecting the basic aspect pointed in our paper - namely, that all computations in the BH conception premise a free fall of substance onto the centre of gravitating body. This is the matter of principle. In fact, Schwarzschilds solution and Landau - Lifshiz solution are not the BH theory. Schwarzschild has distinctively said, which problem and in which approximations (the gravitating body taken as the point) he solved. Landau and Lifshiz said clearly that they neglect the pressure of substance (page 406). If you want to criticise the theory of black holes, you have to address to other works, not to these. I would point again, in GR for a distant observer the body never goes under the event horizon. Well, such your position is a surprise for us. Before, you expressed a basically other opinion: Then you are writing, the radius of gravitating body which in Schwarzschilds problem was infinitesimal. While in fact, in Schwarzschild problem it is considered the centrally symmetrical gravity field created by the spherically symmetrical distribution of substance. So it is absolutely unclear, why it seems to you as if conditions to apply (53) (of our paper - Authors) have not been satisfied. In fact, all conditions have been. Unfortunately for you, we have to mark, neither your
previous opinion nor this position which you are trying to take after our argumentation is
valid. First of all, you agreed that Schwarzschild solved just the problem of point
gravitating body. Well, how could you disagree when the very name of his paper - On
the gravity field of point mass in Einsteinian theory - says of it? Additionally to this, you have admitted that we have to
account the counter-pressure, and even said, Landau - Lifshiz
solutions are not the BH theory. On one hand this shows that you agreed with
our arguments whose account fully disproves the possibility of unlimited collapse of dust
sphere, but on the other hand, we can find alike approach in other literature on BH. For
example, Penrose wrote so: General pattern is well known for
spherically symmetrical body. If the mass was large enough, the finite balanced state does
not exist. After the radiation carries away enough of thermal energy, the body begins to
shrink, and this goes on up to achieving the physical singularity located at r = 0 [9, p. 390].
Furthermore, in the problem of dust sphere Landau uses the same Schwarzschilds
metric without any changes in passing from the outer to inner space of the dust sphere;
this means, he uses the same statement of problem which is applied in the relativistic
modelling of BH. With a great part of stretch we could imagine that Landau considers the
metric of usual gravitating body, but it was namely Landau who wrote: Let us draw our attention that in all cases the moment of passing
the surface of collapsing body under the Schwarzschilds sphere (r ( Speaking of other works, we would like to notice, in the
paper we gave not only the analysis of collapsing dust sphere but also the
Oppenheimers solution for the case of collapse of dying star. We showed that the
condition of zero pressure within the sphere, as well as a non-decelerated fall of
substance to the very centre, is determining for this problem. Developers of the BH
conception widely use Oppenheimers solution and they used to refer to it. Moreover,
in limits of BH conception and keeping at least outward formality, you cannot show us
other conditions, as these conditions are objective in limits of BH modelling. In presence
of counter-pressure, the metric inside the sphere will not be singular at all and its
appearance will not be limited by the change of coefficients. Thus, the grounds on which
Schwarzschild selected his metric disappear. So, even if some today author writes that he
accounts the counter-pressure but uses the Schwarzschilds metric, he will only show
himself to be not objective and, truly speaking, ignorant in physical processes. The
problem described by Landau directly relates to the BH conception and you have no grounds
to say the opposite, even if you want much. At the same time, a considerable transformation of your
opinion that you are denying now Landaus concern to the BH conception speaks only
that our analysis is correct and is deeper than relativists understand these physical
processes. In this item, there was one more issue, which we have to enlighten separately. Citation: I asked you, do you understand the difference in R and r?. Now you have a case to compare your knowledge with the standard mathematical formalism, in accordance with which in the end of problem you have to return to the initial coordinates, to put the solution in correspondence with the conditions of modelling. I am substituting the solution into the
initial equation, in the initial coordinates: the metric appears nonlinear (and I did not
deny it), the metric tends at the infinity to become linear (as it was required). I asked
you: what namely is not true? In your work you wrote on this subject, the conditions (25)
are not true. I reminded you and am reminding again, (25) is that to which the
coefficients have to tend at the infinity - and you wrote in the end of (25): at x1 = If we compare our citation with your answer/question, we will see a clear inconsistency. We said in our citation of necessity to return to the initial metric after having found the solution in the artificially introduced coordinates. Your question relates to the inconsistency in coefficients of final solution and conditions for the determinant that we touched in our paper by the way. It is seen in the form of your respond, you well understand: in the Supplement 1 we gave a proof of absence of any out-of-centre singularity in the Schwarzschilds metric and after this any points of Schwarzschilds derivation become senseless. But we will answer. We have to consider this question in several planes. On
one hand, as we admitted in the previous Supplement, we actually did not account the
condition x1 = But there exists another side of the medal. Furthermore, if speaking of Schwarzschilds mistakes,
you have omitted one more basic point of our previous post to you, which touched the
equatorial location of the point x2
= 0 at which Schwarzschilds sought the
solution. This also is a mistake. Or rather, even not a mistake but a silent substitution
with whose help he could, at all, yield whatever solution. We suggested you to show us the
solution out of this ersatz-equatorial point which, after Schwarzschilds opinion,
had to be identical to that he yielded. Have you a problem? 5. Citation: As to the collapse of dust sphere. I selected you exceptionally because in your first posts you seemed to be different from them. (Sergey, what for do you take this tone?) I already wrote, in GR, for a distant observer a body will never go under the event horizon. What do you dislike, disagree? Or do you know the source of GR where something other was written? As to my tone, these are emotions. |
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(21) |
(giving the time scale) [2, p. 206] and from (16) of the same paper [2, p. 206]: |
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(22) |
In particular, from this second expression it follows that
the light speed is constant and the derivative of |
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(23) |
Doing not touching yet, whether (23) is true (there will
be your related question below), we can conclude that the light speed has to grow in
proportion to the potential. Not in vain we in page 6 of our Supplement 1 raised the
question, is it legal to represent the time parameter as the product of time by the light
speed. With it, the time parameter of 4-D metric depends on spatial coordinates and the
differentiation with respect to this parameter much complicates and becomes irrelevant to
the Schwarzschilds operations. This also is the Schwarzschilds mistake. Gross
mathematical mistake, due to which he got into the discrepancy with Einsteins
formula, in accordance with which the light speed grows with the growing potential. Thus,
when you are trying to find mistakes in our studies, we would be grateful if you first
caught the mistakes in the conception which you defend, doing not accusing the
opponent that he has to do it instead you and at the same time taking offence at him. |