On axially symmetric solutions of Einstein's field equations in matter and an example of static gravitational shielding

A model system, consisting of a thin spherical shell with radiusR and massM and a point massm at a distances>R from the center of the sphere, held fixed by an appropriate strut, is solved to ordermM. The stresses in the shell are not of the canonical Weyl type, and it is argued that the same is true for more realistic situations, e.g., rotating matter. Owing to the nonlinearity of Einstein's field equations, the field of the point mass is shielded from the interior of the shell by a factor lying between 1–3M/R and 1–2M/R, and the field outside the shell explicitly depends onR.