Schwarzschild-de Sitter and Anti-de Sitter Thin-Shell Wormholes and Their Stability

M. Sharif,Saadia Mumtaz

doi:10.1155/2014/639759

Abstract

This paper is devoted to construct Schwarzschild-de Sitter and anti-de Sitter thin-shell wormholes by employing Visser’s cut and paste technique. The Darmois-Israel formalism is adopted to formulate the surface stresses of the shell. We analyze null and weak energy conditions as well as attractive and repulsive characteristics of thin-shell wormholes. We also explore stable and unstable solutions against linear perturbations by taking two different Chaplygin gas models for exotic matter. It is concluded that the stress-energy tensor components violate the null and weak energy conditions indicating the existence of exotic matter at the wormhole throat. Finally, we find unstable and stable configurations for the constructed thin-shell wormholes.

Highlights

A wormhole is a hypothetical region of spacetime which acts as a shortcut connecting different regions of the universe through a handle or tunnel
The violation of null (NEC) and weak energy conditions (WEC) is the fundamental property for traversable wormholes indicating the occurrence of exotic matter which must be fulfilled at the wormhole throat
To support the exotic matter at the wormhole throat, we model wormholes by taking generalized cosmic Chaplygin gas (GCCG) and modified cosmic Chaplygin gas (MCCG) equation of state (EoS) in the following subsections

Summary

Introduction

A wormhole is a hypothetical region of spacetime which acts as a shortcut connecting different regions of the universe through a handle or tunnel. The stable/unstable wormhole models can be analyzed either by taking perturbations around a static solution or by using equation of state (EoS) for exotic matter at the wormhole throat. In this context, Poisson and Visser [8] investigated stable TSWs against linear perturbations formed by joining two different manifolds of the Schwarzschild geometry. Banerjee [24] explored stability formalism for (2+1)-dimensional spherical TSWs by taking phantom energy and Chaplygin gas as an exotic matter. The last section deals with the conclusions of our results

General Formalism

Standard Approach for Stability Analysis

Schwarzschild-de Sitter and Anti-de Sitter Wormholes

Conclusions