The general solution for relativistic spherical shells

TL;DR

This paper derives the general exact solutions for relativistic spherical shells in Einstein's equations, classifying them into physically realistic and exotic phantom-like types, including known special cases.

Contribution

It provides a comprehensive, closed-form classification of solutions for spherically symmetric shells with various equations of state in general relativity.

Findings

Two classes of solutions: physically realistic and phantom-like.

Known linear-barotropic solutions are special cases.

Potential applications in strong field regimes.

Abstract

The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split into two classes: a class of "astro-physically interesting" solutions describing "ordinary" matter with positive density and pressure, and a class of "phantom-like" solutions with positive density but negative active gravitational mass, which can also be of interest in several "very strong fields" regimes. Known results on linear-barotropic equations of state are recovered as particular cases.