SELF 2 S.B. Karavashkin and O.N. Karavashkina
 (11)
 introduce
 (12)
 and yield
 (13)
 You are thinking, we have a right to conclude from (13) that in Newton’s law the singularity is absent. Is it so? No of course. In changing the variable, we above (12) introduce also the domains of its variation. If in our example
 (14)
 then
 (15)
 It follows from (15) that in (13) the singularity will be present but at other values of used variable R . And nothing of surprise that the variable R can take negative values. This is not the measured variable. The measured value is r and for it the requirement of non-negative radius-vector in spherical either polar coordinates is true. The same in Schwarzschild’s problem. Which relation has the Jacobian equal to unity to the return to initial variables? No relation. In the initial metric, there was the variable r. In the final expression Schwarzschild passed to the variable
 (16)
 This means, as in spherical coordinates the radius-vector cannot be negative, there acts the condition similar to (14), and acts namely with respect to r. In accordance with this condition we yield for R
 (17)
 The singularity in the Schwarzschild’s final expression, at the lower limit of domain of r variation, will clearly reveal in new coordinates at
 (18)
 But this does not mean any event horizons out of the centre of gravitating body. The centre in the new coordinate system will be determined by the condition (18), and the domain of R variation
 (19)
 is discrepant to the physical stipulations of the model, as it contradicts the domain of existence of the very variable R. Your difficulty was in misunderstanding this.

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