Expanding and Collapsing Scalar Field Thin Shell

TL;DR

This paper investigates the dynamics of scalar field thin shells in Reissner-Nordström spacetime, deriving junction conditions, solving equations numerically, and analyzing conditions for expansion, collapse, or bouncing behavior.

Contribution

It derives Israel junction conditions for scalar shells in Reissner-Nordström spacetime and provides numerical solutions illustrating their expanding or collapsing behavior.

Findings

Scalar shells can expand to infinity or collapse into singularities.

Massless and massive scalar shells exhibit similar qualitative behaviors.

Explicit scalar potential functions influence shell dynamics and outcomes.

Abstract

This paper deals with the dynamics of scalar field thin shell in the Reissner-Nordstr$\ddot{o}$m geometry. The Israel junction conditions between Reissner-Nordstr$\ddot{o}$m spacetimes are derived, which lead to the equation of motion of scalar field shell and Klien-Gordon equation. These equations are solved numerically by taking scalar field model with the quadratic scalar potential. It is found that solution represents the expanding and collapsing scalar field shell. For the better understanding of this problem, we investigate the case of massless scalar field (by taking the scalar field potential zero). Also, we evaluate the scalar field potential when $p$ is an explicit function of $R$. We conclude that both massless as well as massive scalar field shell can expand to infinity at constant rate or collapse to zero size forming a curvature singularity or bounce under suitable conditions.