Evolution of thin shells in D-dimensional General Relativity

TL;DR

This paper investigates the dynamics of thin spherical shells in D-dimensional Einstein gravity with electromagnetic fields and a cosmological constant, analyzing their evolution, asymptotic behavior, and cosmic censorship.

Contribution

It provides a comprehensive analysis of shell dynamics in higher-dimensional spacetimes, including asymptotic limits and conditions for weak cosmic censorship.

Findings

Shell dynamics depend on the orientation of the gradient of the radial coordinate.

Asymptotic analysis reveals behavior for small and large shell radii.

Weak cosmic censorship is proven for the studied class of solutions.

Abstract

In this paper we consider singular timelike spherical hypersurfaces embedded in a $D$-dimensional spherically symmetric bulk spacetime which is an electrovacuum solution of Einstein equations with cosmological constant. We analyse the different possibilities regarding the orientation of the gradient of the standard $r$ coordinate in relation to the shell. Then we study the dynamics according to Einstein equations for arbitrary matter satisfying the dominant energy condition. In particular, we thoroughly analyse the asymptotic dynamics for both the small and large-shell-radius limits. We also study the main qualitative aspects of the dynamics of shells made of linear barotropic fluids that satisfy the dominant energy condition. Finally, we prove weak cosmic censorship for this class of solutions.