**Authors:** Stephen J. Crothers

The so-called 'Schwarzschild solution' is not Schwarzschild's solution, but a corruption of the Schwarzschild/Droste solution due to David Hilbert (December 1916), wherein m is allegedly the mass of the source of the alleged associated gravitational field and the quantity r is alleged to be able to go down to zero (although no proof of this claim has ever been advanced), so that there are two alleged 'singularities', one at r=2m and another at r=0. It is routinely alleged that r=2m is a 'coordinate' or 'removable' singularity which denotes the so-called 'Schwarzschild radius' (event horizon) and that the 'physical' singularity is at r=0. The quantity r in the usual metric has never been rightly identified by the physicists, who effectively treat it as a radial distance from the alleged source of the gravitational field at the origin of coordinates. The consequence of this is that the intrinsic geometry of the metric manifold has been violated in the procedures applied to the associated metric by which the black hole has been generated. It is easily proven that the said quantity r is in fact the inverse square root of the Gaussian curvature of a spherically symmetric geodesic surface in the spatial section of Schwarzschild spacetime and so does not denote radial distance in the Schwarzschild manifold. With the correct identification of the associated Gaussian curvature it is also easily proven that there is only one singularity associated with all Schwarzschild metrics, of which there is an infinite number that are equivalent. Thus, the standard removal of the singularity at r=2m is actually a removal of the wrong singularity, very simply demonstrated herein.

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[v1] 14 Mar 2011

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