Abstract

It is demonstrated herein that:

1. The quantity 'r' appearing in the so-called 'Schwarzschild solution' is neither a distance nor a geodesic radius in the manifold but is in fact the inverse square root of the Gaussian curvature of the spatial section and does not generally determine the geodesic radial distance (the proper radius) from the centre of spherical symmetry of a 3-D spherically symmetric metric manifold.
2. The Theory of Relativity forbids the existence of point-mass singularities because they imply in nite energies (or equivalently, that a material body can acquire the speed of light in vacuo).
3. R_ic = Ruv = 0 violates Einstein's 'Principle of Equivalence' and so does not describe Einstein's gravitational field.
4. Einstein's conceptions of the conservation and localisation of gravitational energy are invalid.
5. The concepts of black holes and their interactions are ill-conceived.
6. Expansion of the Universe and Big bang cosmology are inconsistent General Relativity.