We show that in this solution there is a singularity at the origin, and give the parameters of that singularity in terms of the geometrical and physical parameters of the shell. This does not correspond to an infinite concentration of matter, but in fact to zero energy density at the center. It does, however, imply that the spacetime within the spherical cavity is not flat, so that there is a non-trivial gravitational field there, in contrast with Newtonian gravitation. This gravitational field is repulsive with respect to the origin, and thus has the effect of stabilizing the geometrical configuration of the matter, since any particle of the matter that wanders out into either one of the vacuum regions tends to be brought back to the bulk of the matter by the gravitational field.
Keywords:
General Relativity, Einstein Equations, Boundary Conditions, Exact Solution.
DOI: 10.5281/zenodo.5087612