Possibility of stable thin-shell around wormholes within the string cloud and quintessential field via the van der Waals and polytropic EOS in General relativity

TL;DR

This paper explores the possibility of stable thin-shell structures around wormholes influenced by string clouds and quintessence fields, using van der Waals and polytropic equations of state within general relativity.

Contribution

It introduces new solutions for wormholes with thin shells under modified matter sources and analyzes their stability using specific equations of state.

Findings

Stable thin-shell solutions are possible around wormholes.

The stability depends on the choice of equation of state.

Physical attributes of the shell are characterized in the presence of string clouds and quintessence.

Abstract

In this work, we present the Einstein field equations (EFE) in the framework of a modified matter source and thus find out the solutions for the Wormhole. To obtain characteristic solutions set, we employ two kinds of equations of states (EOS), i.e., the van der Waals and polytropic EOS to the EFE. We adopt embedding class as a general technique for the system and discuss several physical attributes of the stellar system under embedded wormhole solutions. Detailed discussion about the matter contents of the thin-shell developed around the obtained wormhole solutions in the background of Schwarzschild BH surrounded by cloud and quintessence-type fluid distribution by using a well-known cut and paste approach. We have also performed stability analysis using the linearized radial perturbation method for the van der Waals EOS and polytropic EOS. Several interesting points have evolved from the entire investigation along with the features of the thin shell around the wormhole.