Aspects of spherical shells in a D-dimensional background

TL;DR

This paper constructs and analyzes the stability of spherical shells in D-dimensional spacetimes, examining energy conditions and dynamical evolution through a general formalism, with various examples across dimensions.

Contribution

It introduces a general formalism for the stability analysis of spherical shells in arbitrary dimensions, extending previous work to D-dimensional geometries.

Findings

Weak energy condition constraints derived for shells

Dynamical evolution equations established

Stability conditions formulated for static solutions

Abstract

In this work, shells are mathematically constructed by applying the cut and paste procedure to D-dimensional spherically symmetric geometries. The weak energy condition for the matter on the shells is briefly analyzed. The dynamical evolution is studied, and the general formalism for the stability of static solutions is presented. Several examples corresponding to different spacetime dimensions and values of the parameters are considered.