Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-01-11
Concepts Phys. 3 (2006) 307-318
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTeX, 4 1/2 pages; the order of assumptions changed and new references added
Scientific paper
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.
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