## Concerning Fundamental Mathematical and Physical Defects in the General Theory of Relativity

**Authors:** Stephen J. Crothers

The physicists have misinterpreted the quantity 'r' appearing in the socalled
"Schwarzschild solution" as it is neither a distance nor a geodesic
radius but is in fact the inverse square root of the Gaussian curvature
of a spherically symmetric geodesic surface in the spatial section of
the Schwarzschild manifold, and so it does not directly determine any
distance at all in the Schwarzschild manifold - in other words, it determines
the Gaussian curvature at any point in a spherically symmetric
geodesic surface in the spatial section of the manifold. The concept of
the black hole is consequently invalid. It is also shown herein that the
Theory of Relativity forbids the existence of point-mass singularities
because they imply infinite energies (or equivalently, that a material
body can acquire the speed of light in vacuo), and so the black hole
is forbidden by the Theory of Relativity. That Ric=R_{μν} = 0 violates
Einstein's 'Principle of Equivalence' and so does not describe Einstein's
gravitational field, is demonstrated. It immediately follows that Einstein's
conceptions of the conservation and localisation of gravitational
energy are invalid - the General Theory of Relativity violates the usual
conservation of energy and momentum.

**Comments:** 13 pages

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### Submission history

[v1] 14 Mar 2011

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