Positive energy density in topologically charged exponential wormholes and Regge–Wheeler potential

Abstract

In this paper, we investigate a series of topologically charged exponential traversable wormhole models described by the standard metric form:

$$\begin{aligned}ds^2=-\mathcal {A}^2(r)\,dt^2+\mathcal {B}^2(r)\,\left[ \frac{dr^2}{\alpha ^2}+r^2\,(d\theta ^2+\sin ^2\theta \,d\phi ^2)\right] ,\end{aligned}$$

where \(0< \alpha < 1\) is the global monopole chare parameter. We focus on the positivity of the energy density across these models, defined by the following functions: (i) \(\mathcal {A}(r)=\exp \left( -\frac{M}{r}\right) \) and \(\mathcal {B}(r)=\exp \left( \frac{M}{r}+\beta \,r\right) \), (ii) \(\mathcal {A}(r)=\exp \left( -\frac{M}{r}-\gamma \,r\right) \) and \(\mathcal {B}(r)=\exp \left( \frac{M}{r}\right) \), and (iii) \(\mathcal {A}(r)=\exp \left( -\frac{M}{r}-\gamma \,r\right) \) and \(\mathcal {B}(r)=\exp \left( \frac{M}{r}+\beta \,r\right) \), where \(M, \beta \) and \(\gamma \) are constants. For each model, we evaluate key properties such as the wormhole throat radius, geometric stability, and energy conditions. Additionally, we analyze geodesic motions of test particle around a generalized wormhole, highlighting how the presence of the global monopole parameter affects trajectories of test particles within this topologically charged wormhole. Our results demonstrate that the radius of the wormhole throat is consistent with established characteristics of traversable wormholes and is free from singularities. subsequently, we study the Regge–Wheeler (RW) potential in the context of our chosen wormhole background, providing a detail analysis of its implications for spin zero scalar s-waves with multipole number \(\ell =0\). our analysis shows that the RW potential for spin zero scalar field is influence by the global monopole parameter and the coupling constant, which possesses dimensions inverse to that of length present in the wormhole space-time geometry. This modification has profound implications for the stability and dynamics of scalar perturbations in the vicinity of the wormhole, potentially affecting the stability of the wormhole itself.