  A strict derivation of the Schwarzschild metric, based solely on Newton's law
of free fall and the equivalence principle, is presented. In the light of it,
regarding Schwarzschild's coordinates as representing the point of view of a
distant observer resting relative to the source of a centrally symmetric
gravitational field, proves illegitimate. Such point of view is better
represented by the Painleve-Gullstrand system of coordinates, which agrees with
Schwarzschild's system with respect to its spatial coordinates and time scale,
but disagrees with respect to the relation of simultaneity. A duality of the
Schwarzschild solution and its time-irreversibility is suggested. The physical
meaning of the coordinate singularity at the Schwarzschild radius is clarified.
