Newtonian and General Relativistic Models of Spherical Shells

TL;DR

This paper develops Newtonian and general relativistic models of spherical shells with varying thickness, analyzing their properties and stability to enhance understanding of such structures in astrophysics.

Contribution

It introduces a new family of spherical shell models in both Newtonian and relativistic frameworks, including stability analysis.

Findings

Relativistic shells exhibit equal azimuthal and polar pressures.

Radial pressure is proportional to tangential pressure in these models.

Initial stability assessments of the shells are presented.

Abstract

A family of spherical shells with varying thickness is derived by using a simple Newtonian potential-density pair. Then, a particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian family of shells. The matter of these relativistic shells presents equal azimuthal and polar pressures, while the radial pressure is a constant times the tangential pressure. We also make a first study of stability of both the Newtonian and relativistic families of shells.