Quantum corrected Schwarzschild thin-shell wormhole

Kimet Jusufi

doi:10.1140/epjc/s10052-016-4456-3

Kimet Jusufi

Open Access

https://doi.org/10.1140/epjc/s10052-016-4456-3

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Abstract

Recently, Ali and Khalil \cite{Farag Ali}, based on the Bohmian quantum mechanics derived a quantum corrected version of the Schwarzschild metric. In this paper, we construct a quantum corrected Schwarzschild thin shell wormhole (QSTSW) and investigate the stability of this wormhole. First we compute the surface stress at the wormhole throat by applying the Darmois-Israel formalism to the modified Schwarzschild metric and show that exotic matter is required at the throat to keep the wormhole stable. We then study the stability analysis of the wormhole by considering phantom-energy for the exotic matter, generalized Chaplygin gas (GCG), and the linearized stability analysis. It is argued that, quantum corrections can affect the stability domain of the wormhole.

Highlights

We have constructed a QCTSW by using Visser’s method and shown that exotic matter is required at the throat to keep the wormhole stable
Using the methods of the generalized Chaplygin gas and a linearized stability analysis, we show that the wormhole can be stable by choosing suitable values of parameters
By c√hoosing different values of hin the following interval: 0 < hη/M ≤ 1 it is shown that quantum corrections increase the stability domain of obtaining stable wormhole solutions

Summary

Introduction

Different TSW solutions have been proposed, including, charged TSW [8,9], TSW in heterotic string theory [10], TSW from a noncommutative BTZ black hole [11], TSW in Einstein–Maxwell–Gauss–Bonnet gravity [12], rotating TSW [13,14], TSW from scalar hair black hole [15], TSW supported by normal matter [16,17], cylindrical TSW [18,19,20,21,22,23,24], and TSW with a cosmological constant [25,26], and wormholes in the framework of mimetic gravity; see [27] and the references therein. 2, we start from the quantum corrected Schwarzschild metric and construct a QSTSW by computing the surface stress using the Darmois– Israel formalism. 3, we study the effects of these corrections on the stability of the wormhole by considering, first, the phantom-energy model for the exotic matter, the generalized Chaplygin gas (GCG), and the linearized stability around the static solution. If we write the throat radius a, in terms of the proper time τ on the shell, a = a(τ ), and use the last equation it is not difficult to show that the induced metric on takes the form. One can check that the surface density and the surface pressure are given by the following relations: Page 3 of 7 608 σ.

Phantom-like equation of state

Linearized stability analysis

Conclusion