Neutral thin shell immersed into the Reissner-Nordstr\"om space-time

TL;DR

This paper introduces a new method using effective potential to construct Carter-Penrose diagrams for neutral thin shells in Reissner-Nordström space-time, simplifying the analysis of their global geometry.

Contribution

It presents a novel approach to visualize the global structure of composite space-times with thin shells without extensive analysis.

Findings

Method successfully constructs Carter-Penrose diagrams for various configurations.

Demonstrates applicability to different Reissner-Nordström electro-vacuum manifolds.

Simplifies the analysis of shell dynamics and space-time geometry.

Abstract

Starting from Israel equations for the spherically symmetric thin shells we introduce the effective potential and show how it can be used in constructing, without further thorough investigation, the corresponding Carter-Penrose diagrams describing clearly the global geometry of the composite space-time manifolds. We demonstrate, how this new method works, by considering all possible configurations for the neutral thin dust shell immersed into different types of Reissner-Nordstr\"om electro-vacuum manifolds.