Stability of composite vacuum Heckmann wormholes in Brans-Dicke theory

TL;DR

This study analyzes the stability of composite vacuum Heckmann wormholes in Brans-Dicke gravity under linear perturbations, revealing conditions for stability based on the equation of state parameter and Brans-Dicke parameter.

Contribution

It provides a stability analysis of Heckmann wormholes in Brans-Dicke theory considering linearized perturbations and specific equations of state.

Findings

Wormholes are stable for 0 ≤ β < 1 and all ω except -2.

Stability depends on the equation of state parameter β and the Brans-Dicke parameter ω.

The analysis extends understanding of wormhole stability in alternative gravity theories.

Abstract

This paper discusses linearized (spherically symmetric) perturbation of static Heckmann composite thin shell wormholes in Brans-Dicke gravity. The equation of state $P= \beta^2 \sigma$ at the throat is linearized around the static solution where $\sigma$ energy density of the shell and $P$ the presume. We have shown that this thin shell wormholes is stable within the range $0\leq\beta<1$ and with all values of $\omega$ except $\omega=-2$.