V.5 No 2 3 Supplement 2. The answers to Sergey Khartikov’s 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. Moreover, in this local metric Lorentz transformations have to be true.” Sergey, in presence of gravitation, all solutions of GR have a non-linear metric. In Schwarzschild’s 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 “Schwarzschild’s 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 Einstein’s 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. Einstein also said much that the metric of SR and GR has to be locally linear. You surely well know it, and we said it in our Supplement 1. If the metric was linear, the postulate of constant speed of light is violated. Due to this, the 4-D interval and its invariance lose their sense. Judge for yourself, which sense can be included in the interval
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