# 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.

## Key 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.