This solution is therefore somewhat similar to the one previously found for a spherically symmetric shell of liquid fluid, and is in fact exactly the same in the cases of the inner and outer vacuum regions. The main difference is that here the boundary values and are not chosen arbitrarily, but are instead determined by the dynamics of the system. As was shown in the case of the liquid shell, also in this solution there is a singularity at the origin, that just as in that case does not correspond to an infinite concentration of matter, but in fact to zero matter energy density at the center. Also as in the case of the liquid shell, 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 inner gravitational field has the effect of repelling matter and energy away from the origin, thus avoiding a concentration of matter at that point.
Keywords:
General Relativity, Einstein Equations, Boundary Conditions, Polytropes.
DOI: 10.5281/zenodo.5087723