## The Schwarzschild Solution and Its Implications for Gravitational Waves

**Authors:** Stephen J. Crothers

The so-called 'Schwarzschild solution' is not Schwarzschild's solution, but a corruption,
due to David Hilbert (December 1916), of the Schwarzschild/Droste solution,
wherein m is allegedly the mass of the source of a 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 asserted 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 so-called 'Schwarzschild
solution' has never been rightly identified by the physicists, who, although proposing
many and varied concepts for what r therein denotes, effectively treat it as a radial
distance from the claimed 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. 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 the 'Schwarzschild solution' and so does not in itself define any
distance whatsoever in that 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, in a very
real sense, removal of the wrong singularity, very simply demonstrated herein. This
has major implications for the localisation of gravitational energy i.e. gravitational
waves.

**Comments:** 27 pages

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### Submission history

[v1] 14 Mar 2011

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