Newtonian and General Relativistic Models of Spherical Shells - II

Abstract

A family of potential-density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by inversion transformations of spheres and of the finite shells. We also present a family of double shells with finite thickness. All potential-density pairs are analytical and can be stated in terms of elementary functions. For the above-mentioned structures, we study the circular orbits of test particles and their stability with respect to radial perturbations. All examples presented are found to be stable. A particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian families of spheres and shells. The matter of these structures is anisotropic, and the degree of anisotropy is a function of the radius.