## Geometric and Physical Defects in the Theory of Black Holes

**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.

**Comments:** 12 pages

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### Submission history

[v1] 14 Mar 2011

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